Showing 1–50 of 91 results for author: Mora, C

Monte-Carlo solution of the Kondo model

Authors: Nicolas Paris, Oscar Bouverot-Dupuis, Christophe Mora

Abstract: The Kondo model is a paradigmatic quantum impurity problem realized in a wide variety of experimental platforms and central to the study of strongly correlated electrons. We introduce a discrete model that exactly reproduces the multichannel Kondo model and demonstrate that it can be simulated efficiently. Using cluster Monte Carlo algorithms, we completely eliminate critical slowing down, providi… ▽ More The Kondo model is a paradigmatic quantum impurity problem realized in a wide variety of experimental platforms and central to the study of strongly correlated electrons. We introduce a discrete model that exactly reproduces the multichannel Kondo model and demonstrate that it can be simulated efficiently. Using cluster Monte Carlo algorithms, we completely eliminate critical slowing down, providing direct access to universal crossover functions and transport properties across a broad range of parameters. Remarkably, the same model captures both the weak- and strong-coupling regimes, unifying descriptions traditionally derived in complementary limits and revealing their common origin. Our method naturally accommodates large channel numbers, anisotropy, interacting one-dimensional leads, and channel asymmetry, yielding predictions for transport properties in charge-Kondo devices. △ Less

Submitted 8 July, 2026; originally announced July 2026.

Comments: 7+20 pages, 4+8 figures

Strange Luttinger liquids in a cavity-embedded one-dimensional electronic chain

Authors: Danh-Phuong Nguyen, Christophe Mora, Cristiano Ciuti

Abstract: We study a one-dimensional electronic chain coupled to a homogeneous quantized vacuum field and electron-electron interactions. In the absence of the latter, we derive a low-energy effective description in the presence of light-matter coupling, which we identify as a strange Luttinger liquid. Although it retains a formal resemblance to conventional Luttinger liquid theory, the coupling to the quan… ▽ More We study a one-dimensional electronic chain coupled to a homogeneous quantized vacuum field and electron-electron interactions. In the absence of the latter, we derive a low-energy effective description in the presence of light-matter coupling, which we identify as a strange Luttinger liquid. Although it retains a formal resemblance to conventional Luttinger liquid theory, the coupling to the quantum field qualitatively modifies the low-energy sector and breaks the standard velocity relation underlying Luttinger universality. For finite electron-electron interactions, we recover a phase diagram featuring several phases as a function of interaction strength and hopping amplitude, including a phase hosting Majorana-like zero modes. Using exact diagonalization, we compute observables that characterize the phase boundaries and show that the cavity field significantly shifts them. We also study the fate of Majorana-like states under the influence of the cavity field, highlighting their modification by light-matter coupling. Finally, we investigate whether the strange Luttinger liquid description identified in the noninteracting regime continues to hold when electron-electron interactions are introduced. △ Less

Submitted 1 July, 2026; originally announced July 2026.

Comments: 11 pages, 4 figures

Dispersion of Anyon Bloch Bands

Authors: Kishore Iyer, Andreas Feuerpfeil, Valentin Crépel, Nicolas Regnault, Christophe Mora

Abstract: Fractional Chern insulators (FCIs) are zero magnetic field analogs of fractional quantum Hall states. While the electrons forming an FCI are not subject to an external magnetic field, their anyonic excitations experience a magnetic field with finite-flux due to a many-body Berry phase, whose lattice periodicity generically induces some dispersion. From Laughlin wavefunctions at filling 1/m, we ana… ▽ More Fractional Chern insulators (FCIs) are zero magnetic field analogs of fractional quantum Hall states. While the electrons forming an FCI are not subject to an external magnetic field, their anyonic excitations experience a magnetic field with finite-flux due to a many-body Berry phase, whose lattice periodicity generically induces some dispersion. From Laughlin wavefunctions at filling 1/m, we analytically construct single-anyon Bloch states in an ideal band, providing a basis to efficiently compute the dispersion. The anyon spectrum exhibits an $m$-fold degeneracy in the reduced magnetic Brillouin zone (BZ), which originates from the topological degeneracy of the FCI. From our wavefunctions, we derive the m^2-fold degeneracy seen in previous works, showing it to be a splicing of anyon momenta into the electronic BZ. Finally, we find that the anyon dispersion bandwidth is controlled by quantum geometry non-uniformity, growing linearly at weak modulation and saturating at strong modulation. Remarkably, higher harmonics of the quantum geometry alone strongly suppress the dispersion, which we attribute to emergent magnetic translation symmetries. When combined with the first harmonic, a positive (negative) second harmonic drives the system toward a second- (first-) harmonic-dominated regime, thereby reducing (enhancing) the bandwidth. Our results offer an analytically controlled method for evaluating anyon spectra in ideal band FCI, shedding light on how non-uniform quantum geometry and emergent symmetries shape the dispersion of anyons. △ Less

Submitted 27 April, 2026; originally announced April 2026.

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Authors: Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, Adrian Chapman, Laura Clinton, Marcos Crichigno, Elizabeth Crosson, Toby Cubitt, Charles Derby, Oliver Dowinton, Paul K. Faehrmann, Steve Flammia, Brian Flynn, Filippo Maria Gambetta, Raúl García-Patrón, Max Hunter-Gordon, Glenn Jones, Abhishek Khedkar, Joel Klassen, Michael Kreshchuk, Edward Harry McMullan, Lana Mineh, Ashley Montanaro, Caterina Mora, John J. L. Morton , et al. (10 additional authors not shown)

Abstract: Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of t… ▽ More Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware. △ Less

Submitted 19 December, 2025; v1 submitted 30 October, 2025; originally announced October 2025.

Comments: 94 pages, 76 figures

Fermionic dynamics on a trapped-ion quantum computer beyond exact classical simulation

Authors: Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė, Adrian Chapman, Laura Clinton, Marcos Crichigno, Elizabeth Crosson, Toby Cubitt, Charles Derby, Oliver Dowinton, Norhan Eassa, Paul K. Faehrmann, Steve Flammia, Brian Flynn, Filippo Maria Gambetta, Raúl García-Patrón, Max Hunter-Gordon, Glenn Jones, Abhishek Khedkar, Joel Klassen, Michael Kreshchuk, Edward Harry McMullan, Lana Mineh, Ashley Montanaro, Caterina Mora , et al. (15 additional authors not shown)

Abstract: Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and che… ▽ More Simulation of the time-dynamics of fermionic many-body systems has long been predicted to be one of the key applications of quantum computers. Such simulations -- for which classical methods are often inaccurate -- are critical to advancing our knowledge and understanding of quantum chemistry and materials, underpinning a wide range of fields, from biochemistry to clean-energy technologies and chemical synthesis. However, the performance of all previous digital quantum simulations of fermions has been matched by classical methods, and it has thus far remained unclear whether near-term, intermediate-scale quantum hardware could offer any computational advantage in this area. Here, we implement an efficient quantum simulation algorithm on Quantinuum's System Model H2 trapped-ion quantum computer for the time dynamics of a 56-qubit system that is too complex for exact classical simulation. We focus on the periodic spinful 2D Fermi-Hubbard model and present evidence of spin-charge separation, where the elementary electron's charge and spin decouple. In the limited cases where ground truth is available through exact classical simulation, we find that it agrees with the results we obtain from the quantum device. Employing long-range Wilson operators to study deconfinement of the effective gauge field between spinons and the effective potential between charge carriers, we find behaviour that differs from predictions made by classical tensor network methods. Our results herald the use of quantum computing for simulating strongly correlated electronic systems beyond the capacity of classical computing. △ Less

Submitted 19 December, 2025; v1 submitted 30 October, 2025; originally announced October 2025.

Comments: 47 pages, 42 figures

Universal Crossover in the Three-Channel Charge Kondo Model at High Transparency

Authors: Nicolas Paris, Nicolas Dupuis, Christophe Mora

Abstract: Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we res… ▽ More Quantum impurity models provide a central framework for correlated electron physics, with quantum dots enabling controlled experimental realizations. While their weak-coupling behavior is well understood through mappings to Kondo Hamiltonians, the opposite regime of highly transparent contacts has lacked a controlled theoretical description. Using the functional renormalization group (FRG), we resolve this regime for the three-channel charge Kondo device of Ref.~\cite{iftikhar2018}, benchmarking against conformal field theory by reproducing the universal zero-frequency conductance and, crucially, going beyond it to obtain the full frequency crossover of the conductance and the full temperature crossover of the impurity entropy, together with a continuous line of fixed points for interacting leads. These results establish FRG as a powerful nonperturbative tool for quantum impurity problems in regimes inaccessible to conventional approaches, with direct implications for mesoscopic experiments. △ Less

Submitted 13 February, 2026; v1 submitted 3 September, 2025; originally announced September 2025.

Comments: 7+15 pages, 4+6 figures, published 12 February, 2026

Journal ref: Phys. Rev. Lett. 136, 066501, 12 February, 2026

Robustness of real-space topology in moiré systems

Authors: Kryštof Kolář, Kang Yang, Felix von Oppen, Christophe Mora

Abstract: The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wavefunctions,… ▽ More The appearance of fractional Chern insulators in moiré systems can be rationalized by the presence of a fictitious magnetic field associated with the spatial texture of layer-resolved electronic wavefunctions. Here, we present a systematic study of real-space topology and the associated fictitious magnetic fields in moiré systems. We first show that at the level of individual Bloch wavefunctions, the real-space Chern number, akin to a Pontryagin index, is a fragile marker. It generically vanishes except for specific limits where the Bloch functions exhibit fine-tuned zeroes within the unit cell, such as the chiral limit of twisted bilayer graphene (TBG) or the adiabatic regime of twisted homobilayer transition metal dichalcogenides (TMD). We then show that these limitations do not apply to textures associated with ensembles of Bloch wavefunctions, such as entire bands or the ensemble of states at a given energy. The Chern number of these textures defines a robust topological index protected by a spectral gap. We find that symmetries constrain it to be nonzero for both twisted TMDs and TBG across all twist angles and levels of corrugation, implying experimental signatures in scanning tunneling microscopy measurements. By projection to the band ensemble texture, a single-component Hamiltonian under fictitious magnetic field emerges in a broad regime, enabling a direct comparison of multicomponent bands to Landau-level wavefunctions. We also study real-space topology within the topological heavy fermion model of TBG, finding that the real-space topological features are supported only by the light c-electrons. △ Less

Submitted 21 August, 2026; v1 submitted 30 June, 2025; originally announced July 2025.

Comments: Published version

Journal ref: Phys. Rev. X 16, 031043, 2026

Layer skyrmions for ideal Chern bands and twisted bilayer graphene

Authors: Daniele Guerci, Jie Wang, Christophe Mora

Abstract: Ideal $C=1$ Chern bands exhibit a Landau level correspondence: they factorize as a lowest Landau levels and a spinor wavefunction that spans the layer index. We demonstrate that, in single Dirac moiré models, the spinor develops generally a Skyrme texture in real space with an associated Berry phase which compensates exactly the magnetic phase of the Landau level. For ideal bands with higher Chern… ▽ More Ideal $C=1$ Chern bands exhibit a Landau level correspondence: they factorize as a lowest Landau levels and a spinor wavefunction that spans the layer index. We demonstrate that, in single Dirac moiré models, the spinor develops generally a Skyrme texture in real space with an associated Berry phase which compensates exactly the magnetic phase of the Landau level. For ideal bands with higher Chern numbers $C>1$, we find that $C$ color Landau levels are carried by $C$ spinors with Skyrme textures. We identify a SU(C) gauge symmetry in the color space of spinors and an emergent non-Abelian connection in real space intimately linked to the Pontryagin winding index of the layer skyrmions. They result in a total real-space Chern number of $-1$, screening the magnetic phase, irrespective of $C$ and of the number of layers. The topologically robust Skyrme texture remains remarkably intact in twisted bilayer graphene, even far from the chiral limit, and for realistic values of corrugation, making it an experimentally testable feature. We verify our predictions at the first magic angle of twisted bilayer, trilayer, and monolayer-bilayer graphene. △ Less

Submitted 22 August, 2024; originally announced August 2024.

Comments: 8+13 pages, 6 figures

Resilience of the quantum critical line in the Schmid transition

Authors: Nicolas Paris, Luca Giacomelli, Romain Daviet, Cristiano Ciuti, Nicolas Dupuis, Christophe Mora

Abstract: Schmid predicted that a single Josephson junction coupled to a resistive environment undergoes a quantum phase transition to an insulating phase when the shunt resistance $R$ exceeds the resistance quantum $h/(4 e^ 2)$. Recent measurements and theoretical studies have sparked a debate on whether the location of this transition depends on the ratio between the Josephson and the charging energies. W… ▽ More Schmid predicted that a single Josephson junction coupled to a resistive environment undergoes a quantum phase transition to an insulating phase when the shunt resistance $R$ exceeds the resistance quantum $h/(4 e^ 2)$. Recent measurements and theoretical studies have sparked a debate on whether the location of this transition depends on the ratio between the Josephson and the charging energies. We employ a combination of multiple innovative analytical and numerical techniques, never before explicitly applied to this problem, to decisively demonstrate that the transition line between superconducting and insulating behavior is indeed independent of this energy ratio. First, we apply field-theory renormalization group methods and find that the $β$ function vanishes along the critical line up to the third order in the Josephson energy. We then identify a simple fermionic model that precisely captures the low-energy physics on the critical line, regardless of the energy ratio. This conformally invariant fermionic model is verified by comparing the expected spectrum with exact diagonalization calculations of the resistively shunted Josephson junction, showing excellent agreement even for moderate system sizes. Importantly, this identification provides a rigorous non-perturbative proof that the transition line is maintained at $R=h/(4 e^ 2)$ for all ratios of Josephson to charging energies. The line is further resilient to other ultraviolet cutoffs such as the plasma frequency of the resistive environment. Finally, we implement an adiabatic approach to validate the duality at large Josephson energy. △ Less

Submitted 26 March, 2025; v1 submitted 1 July, 2024; originally announced July 2024.

Comments: 11+5 pages, 7+2 figures Published 14 February, 2025

Journal ref: Phys. Rev. B 111, 064509 (2025)

Hofstadter spectrum of Chern bands in twisted transition metal dichalcogenides

Authors: Kryštof Kolář, Kang Yang, Felix von Oppen, Christophe Mora

Abstract: We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of WSe$_2$, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field dependent spectra of WSe$_2$ based on the p… ▽ More We study the topological bands in twisted bilayer transition metal dichalcogenides in an external magnetic field. We first focus on a paradigmatic model of WSe$_2$, which can be described in an adiabatic approximation as particles moving in a periodic potential and an emergent periodic magnetic field with nonzero average. We understand the magnetic-field dependent spectra of WSe$_2$ based on the point net zero flux, at which the external field cancels the average emergent field. At this point, the band structure interpolates between the tightly-bound and nearly-free (weak periodic potential) paradigms as the twist angle increases. For small twist angles, the energy levels in a magnetic field mirror the Hofstadter butterfly of the Haldane model. For larger twist angles, the isolated Chern band at zero flux evolves from nearly-free bands at the point of net zero flux. We also apply our framework to a realistic model of twisted bilayer MoTe$_2$, which has recently been suggested to feature higher Landau level analogs. We show that at negative unit flux per unit cell, the bands exhibit remarkable similarity to a backfolded parabolic dispersion, even though the adiabatic approximation is inapplicable. This backfolded parabolic dispersion naturally explains the similarity of the Chern bands at zero applied flux to the two lowest Landau levels, offering a simple picture supporting the emergence of non-Abelian states in twisted bilayer MoTe$_2$. We propose the study of magnetic field dependent band structures as a versatile method to investigate the nature of topological bands and identify Landau level analogs. △ Less

Submitted 9 September, 2024; v1 submitted 10 June, 2024; originally announced June 2024.

Comments: Published version

Journal ref: Phys. Rev. B 110, 115114 (2024)

Helical trilayer graphene in magnetic field: Chern mosaic and higher Chern number ideal flat bands

Authors: Anushree Datta, Daniele Guerci, Mark O. Goerbig, Christophe Mora

Abstract: Helical trilayer graphene (hTG) exhibits a supermoiré pattern with large domains centered around stacking points ABA and BAB, where two well-separated low-energy bands appear with different total Chern numbers at each valley, forming a Chern mosaic pattern. In the chiral limit, the low-energy bands become exactly flat at zero energy for magic-angle twists. Here we investigate these zero-energy fla… ▽ More Helical trilayer graphene (hTG) exhibits a supermoiré pattern with large domains centered around stacking points ABA and BAB, where two well-separated low-energy bands appear with different total Chern numbers at each valley, forming a Chern mosaic pattern. In the chiral limit, the low-energy bands become exactly flat at zero energy for magic-angle twists. Here we investigate these zero-energy flat bands and their topological properties in the presence of a perpendicular magnetic field. We show that hTG retains the precise flatness of the zero-energy bands, even at finite magnetic fields. We find topological phase transitions at fields corresponding to unit and half magnetic flux leading to an emergence of higher Chern number flat bands. Consequently the Chern mosaic gets modified for finite magnetic fields. We further find the analytical forms of zero-energy wave functions and identify a set of hidden wave functions, which gives crucial insights into both the topological transitions and enhancement of Chern numbers across them. We also find topological transitions away from the chiral limit with finite corrugations and at different magic angles. △ Less

Submitted 22 July, 2024; v1 submitted 23 April, 2024; originally announced April 2024.

Comments: 16 pages, 7 figures

Signature of anyonic statistics in the integer quantum Hall regime

Authors: P. Glidic, I. Petkovic, C. Piquard, A. Aassime, A. Cavanna, Y. Jin, U. Gennser, C. Mora, D. Kovrizhin, A. Anthore, F. Pierre

Abstract: Anyons are exotic low-dimensional quasiparticles whose unconventional quantum statistics extends the binary particle division into fermions and bosons. The fractional quantum Hall regime provides a natural host, with first convincing anyon signatures recently observed through interferometry and cross-correlations of colliding beams. However, the fractional regime is rife with experimental complica… ▽ More Anyons are exotic low-dimensional quasiparticles whose unconventional quantum statistics extends the binary particle division into fermions and bosons. The fractional quantum Hall regime provides a natural host, with first convincing anyon signatures recently observed through interferometry and cross-correlations of colliding beams. However, the fractional regime is rife with experimental complications, such as an anomalous tunneling density of states, which impede the manipulation of anyons. Here we show experimentally that the canonical integer quantum Hall regime can provide a robust anyon platform. Exploiting the Coulomb interaction between two co-propagating quantum Hall channels, an electron injected into one channel splits into two fractional charges behaving as abelian anyons. Their unconventional statistics is revealed by negative cross-correlations between dilute quasiparticle beams. Similarly to fractional quantum Hall observations, we show that the negative signal stems from a time-domain braiding process, here involving the incident fractional quasiparticles and spontaneously generated electron-hole pairs. Beyond the dilute limit, a theoretical understanding is achieved via the edge magnetoplasmon description of interacting integer quantum Hall channels. Our findings establish that, counter-intuitively, the integer quantum Hall regime provides a platform of choice for exploring and manipulating quasiparticles with fractional quantum statistics. △ Less

Submitted 12 September, 2024; v1 submitted 11 January, 2024; originally announced January 2024.

Comments: 6 pages, 4 figures, Methods, Supplemental Information

Journal ref: Nat. Commun. 15, 6578 (2024)

Topological protection of Majorana polaritons in a cavity

Authors: Zeno Bacciconi, Gian Marcello Andolina, Christophe Mora

Abstract: Cavity embedding is an emerging paradigm for the control of quantum matter, offering avenues to manipulate electronic states and potentially drive topological phase transitions. In this work, we address the stability of a one-dimensional topological superconducting phase to the vacuum quantum fluctuations brought by a global cavity mode. By employing a quasi-adiabatic analytical approach completed… ▽ More Cavity embedding is an emerging paradigm for the control of quantum matter, offering avenues to manipulate electronic states and potentially drive topological phase transitions. In this work, we address the stability of a one-dimensional topological superconducting phase to the vacuum quantum fluctuations brought by a global cavity mode. By employing a quasi-adiabatic analytical approach completed by density matrix renormalization group calculations, we show that the Majorana end modes evolve into composite polaritonic modes while maintaining the topological order intact and robust to disorder. These Majorana polaritons keep their non-abelian exchange properties and protect a twofold exponentially degenerate ground state for an open chain. △ Less

Submitted 13 September, 2023; originally announced September 2023.

Comments: 7 pages, 4 figures + supplementary material. Comments are welcome

Journal ref: Phys. Rev. B 109, 165434 (2024)

Nature of even and odd magic angles in helical twisted trilayer graphene

Authors: Daniele Guerci, Yuncheng Mao, Christophe Mora

Abstract: Helical twisted trilayer graphene exhibits zero-energy flat bands with large degeneracy in the chiral limit. The flat bands emerge at a discrete set of magic twist angles and feature properties intrinsically distinct from those realized in twisted bilayer graphene. Their degeneracy and the associated band Chern numbers depend on the parity of the magic angles. Two degenerate flat bands with Chern… ▽ More Helical twisted trilayer graphene exhibits zero-energy flat bands with large degeneracy in the chiral limit. The flat bands emerge at a discrete set of magic twist angles and feature properties intrinsically distinct from those realized in twisted bilayer graphene. Their degeneracy and the associated band Chern numbers depend on the parity of the magic angles. Two degenerate flat bands with Chern numbers $C_A=2$ and $C_B=-1$ arise at odd magic angles, whereas even magic angles display four flat bands, with Chern number $C_{A/B}=\pm1$, together with a Dirac cone crossing at zero energy. All bands are sublattice polarized. We demonstrate the structure behind these flat bands and obtain analytical expressions for the wavefunctions in all cases. Each magic angle is identified with the vanishing of a zero-mode wavefunction at high-symmetry position and momentum. The whole analytical structure results from whether the vanishing is linear or quadratic for the, respectively, odd and even magic angle. The $C_{3z}$ and $C_{2y}T$ symmetries are shown to play a key role in establishing the flat bands. In contrast, the particle-hole symmetry is not essential, except from gapping out the crossing Dirac cone at even magic angles. △ Less

Submitted 4 August, 2023; originally announced August 2023.

Comments: 14 pages, 6 figures

Chern mosaic and ideal flat bands in equal-twist trilayer graphene

Authors: Daniele Guerci, Yuncheng Mao, Christophe Mora

Abstract: We study trilayer graphene arranged in a staircase stacking configuration with equal consecutive twist angle. On top of the moiré cristalline pattern, a supermoiré long-wavelength modulation emerges that we treat adiabatically. For each valley, we find that the two central bands are topological with Chern numbers $C=\pm 1$ forming a Chern mosaic at the supermoiré scale. The Chern domains are cente… ▽ More We study trilayer graphene arranged in a staircase stacking configuration with equal consecutive twist angle. On top of the moiré cristalline pattern, a supermoiré long-wavelength modulation emerges that we treat adiabatically. For each valley, we find that the two central bands are topological with Chern numbers $C=\pm 1$ forming a Chern mosaic at the supermoiré scale. The Chern domains are centered around the high-symmetry stacking points ABA or BAB and they are separated by gapless lines connecting the AAA points, where the spectrum is fully connected. In the chiral limit and at a magic angle of $θ\sim 1.69^\circ$, we prove that the central bands are exactly flat with ideal quantum curvature at ABA and BAB. Furthermore, we decompose them analytically as a superposition of an intrinsic color-entangled state with $\pm 2$ and a Landau level state with Chern number $\mp 1$. To connect with experimental configurations, we also explore the non-chiral limit with finite corrugation and find that the topological Chern mosaic pattern is indeed robust and the central bands are still well separated from remote bands. △ Less

Submitted 5 May, 2023; originally announced May 2023.

Comments: 7+7 pages, 5 figures

Anyonic exchange in a beam splitter

Authors: Christophe Mora

Abstract: The exotic braiding of anyons is certainly the most tantalizing aspect of fractional quantum Hall states. Although braiding is usually thought as a two-dimensional adiabatic manipulation, the braiding phase can also be captured in one dimension in an out-of-equilibrium setting. We discuss here to what extend a beam splitter reveals the braiding phase when excited with voltage or current pulses. We… ▽ More The exotic braiding of anyons is certainly the most tantalizing aspect of fractional quantum Hall states. Although braiding is usually thought as a two-dimensional adiabatic manipulation, the braiding phase can also be captured in one dimension in an out-of-equilibrium setting. We discuss here to what extend a beam splitter reveals the braiding phase when excited with voltage or current pulses. We identify two main physical mechanisms that govern the sign and the size of the output cross-correlations: the non-linearity, characterized by the tunneling exponent, and the presence of holes in the incoming beams, related to the braiding phase. We show how the incoming signals form an environment for the beam splitter (akin to the dynamical Coulomb blockade effect) and thus interpret the mixing not as a collision of particles, but as a collision or interference of waves. We illustrate the physical picture with various examples of excitations for integer and fractional Hall states and show the emergence of genuine antibunching statistics when mixing dense voltage pulses. △ Less

Submitted 9 December, 2022; originally announced December 2022.

Comments: 9 pages, 4 figures

Supermoiré low-energy effective theory of twisted trilayer graphene

Authors: Yuncheng Mao, Daniele Guerci, Christophe Mora

Abstract: Stacking three monolayers of graphene with a twist generally produces two moiré patterns. A moiré of moiré structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moiré lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the… ▽ More Stacking three monolayers of graphene with a twist generally produces two moiré patterns. A moiré of moiré structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moiré lengthscale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\bf Γ}_M$ point of the moiré Brillouin zone and two weakly gapped points at ${\bf K}_M$ and ${\bf K}'_M$. The velocities and small gaps exhibit a spatial dependence in the moiré-of-moiré unit cell, entailing a non-abelian connection potential which ensures gauge invariance. The resulting model is numerically solved and a fully connected spectrum is obtained, which is protected by the combination of time-reversal and twofold-rotation symmetries. △ Less

Submitted 20 March, 2023; v1 submitted 20 October, 2022; originally announced October 2022.

Comments: 17 pages, 15 figures

$\mathbb{Z}_3$ parafermion in the double charge-Kondo model

Authors: D. B. Karki, Edouard Boulat, Winston Pouse, David Goldhaber-Gordon, Andrew K. Mitchell, Christophe Mora

Abstract: Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulo… ▽ More Quantum impurity models with frustrated Kondo interactions can support quantum critical points with fractionalized excitations. Recent experiments [arXiv:2108.12691] on a circuit containing two coupled metal-semiconductor islands exhibit transport signatures of such a critical point. Here we show using bosonization that the double charge-Kondo model describing the device can be mapped in the Toulouse limit to a sine-Gordon model. Its Bethe-ansatz solution shows that a $\mathbb{Z}_3$ parafermion emerges at the critical point, characterized by a fractional $\tfrac{1}{2}\ln(3)$ residual entropy, and scattering fractional charges $e/3$. We also present full numerical renormalization group calculations for the model and show that the predicted behavior of conductance is consistent with experimental results. △ Less

Submitted 9 May, 2023; v1 submitted 10 October, 2022; originally announced October 2022.

Comments: 5 pages+, 3 figures

Journal ref: Phys. Rev. Lett. 130, 146201 (2023)

Observation of edge magnetoplasmon squeezing in a quantum Hall conductor

Authors: H. Bartolomei, R. Bisognin, H. Kamata, J. -M. Berroir, E. Bocquillon, G. Ménard, B. Plaçais, A. Cavanna, U. Gennser, Y. Jin, P. Degiovanni, C. Mora, G. Fève

Abstract: Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance ($Z_0 \approx 50 Ω$) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the qu… ▽ More Squeezing of the quadratures of the electromagnetic field has been extensively studied in optics and microwaves. However, previous works focused on the generation of squeezed states in a low impedance ($Z_0 \approx 50 Ω$) environment. We report here on the demonstration of the squeezing of bosonic edge magnetoplasmon modes in a quantum Hall conductor whose characteristic impedance is set by the quantum of resistance ($R_K \approx 25 k Ω$), offering the possibility of an enhanced coupling to low-dimensional quantum conductors. By applying a combination of dc and ac drives to a quantum point contact, we demonstrate squeezing and observe a noise reduction 18\% below the vacuum fluctuations. This level of squeezing can be improved by using more complex conductors, such as ac driven quantum dots or mesoscopic capacitors. △ Less

Submitted 9 October, 2022; originally announced October 2022.

Comments: 6+2 pages, 3+1 figures

Strain Disorder and Gapless Intervalley Coherent Phase in Twisted Bilayer Graphene

Authors: Gal Shavit, Kryštof Kolář, Christophe Mora, Felix von Oppen, Yuval Oreg

Abstract: Correlated insulators are frequently observed in magic angle twisted bilayer graphene at even fillings of electrons or holes per moiré unit-cell. Whereas theory predicts these insulators to be intervalley coherent excitonic phases, the measured gaps are routinely much smaller than theoretical estimates. We explore the effects of random strain variations on the intervalley coherent phase, which hav… ▽ More Correlated insulators are frequently observed in magic angle twisted bilayer graphene at even fillings of electrons or holes per moiré unit-cell. Whereas theory predicts these insulators to be intervalley coherent excitonic phases, the measured gaps are routinely much smaller than theoretical estimates. We explore the effects of random strain variations on the intervalley coherent phase, which have a pair-breaking effect analogous to magnetic disorder in superconductors. We find that the spectral gap may be strongly suppressed by strain disorder, or vanish altogether, even as intervalley coherence is maintained. We discuss predicted features of the tunneling density of states, show that the activation gap measured in transport experiments corresponds to the diminished gap, and thus offer a solution for the apparent discrepancy between the theoretical and experimental gaps. △ Less

Submitted 14 February, 2023; v1 submitted 7 August, 2022; originally announced August 2022.

Comments: 5 pages, 4 figures + Supplementary. Published version

Journal ref: Phys. Rev. B 107, L081403 (2023)

Anderson's theorem for correlated insulating states in twisted bilayer graphene

Authors: Kryštof Kolář, Gal Shavit, Christophe Mora, Yuval Oreg, Felix von Oppen

Abstract: The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against loca… ▽ More The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under $\mathcal{PT}$, where $\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time reversal, respectively. In contrast, $\mathcal{PT}$-even perturbations will in general induce subgap states and reduce or even eliminate the gap. We use this result to classify the stability of the K-IVC state against various experimentally relevant perturbations. The existence of an Anderson theorem singles out the K-IVC state from other possible insulating ground states. △ Less

Submitted 22 July, 2022; originally announced July 2022.

Comments: 5 pages

Two-sites quantum island in the quasi-ballistic regime

Authors: Deepak B. Karki, Edouard Boulat, Christophe Mora

Abstract: Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a m… ▽ More Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with the experimental findings, and discuss the competition between Kondo-like screening of each individual island and the cooperative transfer of electrons between them. We further predict that the device operated at finite voltage bias produces fractional charges $e^* =e/3$ and propose a generalization to $N$ islands with the fractional charge $e^* =e/(N+1)$. △ Less

Submitted 18 April, 2022; originally announced April 2022.

Comments: 12 pages, 8 figures

Fractionalization and anyonic statistics in the integer quantum Hall collider

Authors: Tom Morel, June-Young M. Lee, H. -S. Sim, Christophe Mora

Abstract: One remarkable feature of strongly correlated systems is the phenomenon of fractionalization where quasiparticles carry only a fraction of the charge or spin of the elementary constituents. Such quasiparticles often present anyonic statistics in two dimensions and lie at the heart of the fractional quantum Hall effect. We discuss the observation of fractionalization and anyonic statistics already… ▽ More One remarkable feature of strongly correlated systems is the phenomenon of fractionalization where quasiparticles carry only a fraction of the charge or spin of the elementary constituents. Such quasiparticles often present anyonic statistics in two dimensions and lie at the heart of the fractional quantum Hall effect. We discuss the observation of fractionalization and anyonic statistics already in the integer quantum Hall effect coupled to a metallic island. A continuous fractional emitter is proposed, which sends dilute beams of non-integer charges, and its full counting statistics is obtained. The fractional charge is governed solely by the number of ballistic channels covered by the island and it is one half of the electron charge for a single ballistic channel. We further characterize the mixing of two such fractional beams through a quantum point contact beam splitter. We predict negative cross-correlations, in strong contrast with free electrons, that depend on the double exchange phase between electrons and the fractional charges emulating anyons. The result is similar to a genuine fractional edge state as recently measured at filling $ν= 1/3$. We revisit the physical interpretation of this experiment and point towards a direct braiding measurement rather than a deviation from fermionic antibunching. △ Less

Submitted 16 May, 2022; v1 submitted 26 October, 2021; originally announced October 2021.

Comments: 19 pages, 7 figures

Journal ref: Phys. Rev. B 105, 075433 (2022)

Quantum magnetism and topological superconductivity in Yu-Shiba-Rusinov chains

Authors: Jacob F. Steiner, Christophe Mora, Katharina J. Franke, Felix von Oppen

Abstract: Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended $t-J$ model for dilute quantum Y… ▽ More Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended $t-J$ model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra. We explore the implications of quantum magnetism for the formation of a topological superconducting phase, contrasting it to existing models assuming classical spin textures. △ Less

Submitted 30 June, 2021; originally announced July 2021.

Comments: 16 pages including supplementary information; 4 figures

Higher-order van Hove singularity in magic-angle twisted trilayer graphene

Authors: Daniele Guerci, Pascal Simon, Christophe Mora

Abstract: We study the presence of higher-order van Hove singularities in mirror-symmetric twisted trilayer graphene. This geometry has recently emerged experimentally as a fascinating playground for studying correlated and exotic superconducting phases. We find that the trilayer hosts a zero-energy higher-order van Hove singularity with an exponent -1/3. The singularity is protected by the threefold rotati… ▽ More We study the presence of higher-order van Hove singularities in mirror-symmetric twisted trilayer graphene. This geometry has recently emerged experimentally as a fascinating playground for studying correlated and exotic superconducting phases. We find that the trilayer hosts a zero-energy higher-order van Hove singularity with an exponent -1/3. The singularity is protected by the threefold rotation symmetry and a combined mirror-particle-hole symmetry and it can be tuned with only the twist angle and a perpendicular electric field. It arises from the combined merging of van Hove singularities and Dirac cones at zero energy, beyond the recent classifications of van Hove singularities. Moreover, we find that varying a third parameter such as corrugation brings the system to a topological Lifshitz transition, with anomalous exponent -2/5, separating regions of locally open and closed semiclassical orbits. △ Less

Submitted 27 July, 2022; v1 submitted 28 June, 2021; originally announced June 2021.

Comments: 18 pages, 13 figures

Journal ref: Phys. Rev. Research 4, L012013 (2022)

Dynamical Coulomb blockade under a temperature bias

Authors: H. Duprez, F. Pierre, E. Sivre, A. Aassime, F. D. Parmentier, A. Cavanna, A. Ouerghi, U. Gennser, I. Safi, C. Mora, A. Anthore

Abstract: We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel submitted to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with… ▽ More We observe and comprehend the dynamical Coulomb blockade suppression of the electrical conductance across an electronic quantum channel submitted to a temperature difference. A broadly tunable, spin-polarized Ga(Al)As quantum channel is connected on-chip, through a micron-scale metallic node, to a linear $RC$ circuit. The latter is made up of the node's geometrical capacitance $C$ in parallel with an adjustable resistance $R\in \{1/2,1/3,1/4\}\times h/e^2$ formed by 2--4 quantum Hall channels. The system is characterized by three temperatures: a temperature of the electrons in the large electrodes ($T$) and in the node ($T_\mathrm{node}$), and a temperature of the electromagnetic modes of the $RC$ circuit ($T_\mathrm{env}$). The temperature in the node is selectively increased by local Joule dissipation, and characterized from current fluctuations. For a quantum channel in the tunnel regime, a close match is found between conductance measurements and tunnel dynamical Coulomb blockade theory. In the opposite near ballistic regime, we develop a theory that accounts for different electronic and electromagnetic bath temperatures, again in very good agreement with experimental data. Beyond these regimes, for an arbitrary quantum channel set in the far out-of-equilibrium situation where the temperature in the node significantly exceeds the one in the large electrodes, the equilibrium (uniform temperature) prediction for the conductance is recovered, albeit at a rescaled temperature $αT_\mathrm{node}$. △ Less

Submitted 8 April, 2021; originally announced April 2021.

Comments: Submitted

Journal ref: Phys. Rev. Research 3, 023122 (2021)

Moiré lattice effects on the orbital magnetic response of twisted bilayer graphene and Condon instability

Authors: Daniele Guerci, Pascal Simon, Christophe Mora

Abstract: We analyze the orbital magnetic susceptibility from the band structure of twisted bilayer graphene. Close to charge neutrality, the out-of-plane susceptibility inherits the strong diamagnetic response from graphene. Increasing the doping, a crossover from diamagnetism to paramagnetism is obtained and a logarithmic divergence develops at the van Hove singularity of the Moiré lattice in the first ba… ▽ More We analyze the orbital magnetic susceptibility from the band structure of twisted bilayer graphene. Close to charge neutrality, the out-of-plane susceptibility inherits the strong diamagnetic response from graphene. Increasing the doping, a crossover from diamagnetism to paramagnetism is obtained and a logarithmic divergence develops at the van Hove singularity of the Moiré lattice in the first band. The enhanced paramagnetism at the van Hove singularity is stronger for relatively large angle but gets suppressed by the flat spectrum towards the vicinity of the first magic angle. A diverging paramagnetic susceptibility indicates an instability towards orbital ferromagnetism with an orbital out-of-plane magnetization and a Landau level structure. The region of instability is however found to be practically very small, parametrically suppressed by the ratio of the electron velocity to the speed of light. We also discuss the in-plane orbital susceptibility at charge neutrality where we find a paramagnetic response and a logarithmic divergence at the magic angle. The paramagnetic response is associated with negative counterflow current in the two layers and does not admit a semiclassical description. △ Less

Submitted 7 July, 2021; v1 submitted 24 March, 2021; originally announced March 2021.

Comments: 19 pages, 13 figures

Journal ref: Phys. Rev. B 103, 224436 (2021)

Superradiant phase transition in electronic systems and emergent topological phases

Authors: Daniele Guerci, Pascal Simon, Christophe Mora

Abstract: We derive a general criterion for determining the onset of superradiant phase transition in electronic bands coupled to a cavity field, with possibly electron-electron interactions. For longitudinal superradiance in 2D or genuine 1D systems, we prove that it is always prevented, thereby extending existing no-go theorems. Instead, a superradiant phase transition can occur to a nonuniform transverse… ▽ More We derive a general criterion for determining the onset of superradiant phase transition in electronic bands coupled to a cavity field, with possibly electron-electron interactions. For longitudinal superradiance in 2D or genuine 1D systems, we prove that it is always prevented, thereby extending existing no-go theorems. Instead, a superradiant phase transition can occur to a nonuniform transverse cavity field and we give specific examples in non-interacting models, either through Fermi surface nesting or parabolic band touching. Investigating the resulting time-reversal symmetry breaking superradiant states, we find in the former case Fermi surface lifting down to four Dirac points on a square lattice model, with topologically protected zero-modes, and in the latter case topological bands with non-zero Chern number on an hexagonal lattice. △ Less

Submitted 18 May, 2020; originally announced May 2020.

Comments: 6 pages, 2 figures and supplementary material

Journal ref: Phys. Rev. Lett. 125, 257604 (2020)

Phase-Coherent Dynamics of Quantum Devices With Local Interactions

Authors: Michele Filippone, Arthur Marguerite, Karyn Le Hur, Gwendal Fève, Christophe Mora

Abstract: This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving Coulomb-induced quantum state transfer. Extending to out-of-eq… ▽ More This review illustrates how Local Fermi Liquid (LFL) theories describe the strongly correlated and coherent low-energy dynamics of quantum dot devices. This approach consists in an effective elastic scattering theory, accounting exactly for strong correlations. Here, we focus on the mesoscopic capacitor and recent experiments achieving Coulomb-induced quantum state transfer. Extending to out-of-equilibrium regimes, aiming at triggered single electron emission, we illustrate how inelastic effects become crucial, requiring approaches beyond LFLs, shedding new light on past experimental data, by showing clear interaction effects in the dynamics of mesoscopic capacitors. △ Less

Submitted 31 August, 2020; v1 submitted 15 April, 2020; originally announced April 2020.

Comments: 54 pages, 17 Figures

Journal ref: Entropy 2020, 22(8), 847

Double-periodic Josephson junctions in a quantum dissipative environment

Authors: Tom Morel, Christophe Mora

Abstract: Embedded in an ohmic environment, the Josephson current peak can transfer part of its weight to finite voltage and the junction becomes resistive. The dissipative environment can even suppress the superconducting effect of the junction via a quantum phase transition occuring when the ohmic resistance $R_s$ exceeds the quantum resistance $R_{q}=h/(2e)^2$. For a topological junction hosting Majorana… ▽ More Embedded in an ohmic environment, the Josephson current peak can transfer part of its weight to finite voltage and the junction becomes resistive. The dissipative environment can even suppress the superconducting effect of the junction via a quantum phase transition occuring when the ohmic resistance $R_s$ exceeds the quantum resistance $R_{q}=h/(2e)^2$. For a topological junction hosting Majorana bound states with a $4 π$ periodicity of the superconducting phase, the phase transition is shifted to $4 R_{q}$. We consider a Josephson junction mixing the $2 π$ and $4 π$ periodicities shunted by a resistor, with a resistance between $R_q$ and $4 R_q$. Starting with a quantum circuit model, we derive the non-monotonic temperature dependence of its differential resistance resulting from the competition between the two periodicities; the $4 π$ periodicity dominating at the lowest temperatures. The non-monotonic behaviour is first revealed by straightforward perturbation theory and then substantiated by a fermionization to exactly solvable models when $R_s=2R_{q}$: the model is mapped onto a helical wire coupled to a topological superconductor when the Josephson energy is small and to the Emery-Kivelson line of the two-channel Kondo model in the opposite case. △ Less

Submitted 9 April, 2019; originally announced April 2019.

Flat bands and perfect metal in trilayer moiré graphene

Authors: Christophe Mora, Nicolas Regnault, B. Andrei Bernevig

Abstract: We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational… ▽ More We investigate the electronic structure of a twisted multilayer graphene system forming a moiré pattern. We consider small twist angles separating the graphene sheets and develop a low-energy theory to describe the coupling of Dirac Bloch states close to the K point in each individual plane. Extending beyond the bilayer case, we show that, when the ratio of the consecutive twist angles is rational, a periodicity emerges in quasimomentum space with moiré Bloch bands even when the system does not exhibit a crystalline lattice structure in real space. For a trilayer geometry, we find flat bands in the spectrum at certain rotation angles. Performing a symmetry analysis of the band model for the trilayer, we prove that the system is a perfect metal in the sense that it is gapless at all energies. This striking result originates from the three Dirac cones which can only gap in pairs and produce bands with an infinite connectivity. The full gapless property is protected by an emergent particle-hole symmetry valid at sufficiently small angles. △ Less

Submitted 16 January, 2019; originally announced January 2019.

Comments: 4+6 pages, 2+3 figures

Journal ref: Phys. Rev. Lett. 123, 026402 (2019)

4$π$ and 8$π$ dual Josephson effects induced by symmetry defects

Authors: Corneliu Malciu, Leonardo Mazza, Christophe Mora

Abstract: In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$π$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$π$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconduc… ▽ More In topological insulator edges, the duality between the Zeeman field orientation and the proximitized superconducting phase has been recently exploited to predict a magneto-Josephson effect with a 4$π$ periodicity. We revisit this latter Josephson effect in the light of this duality and show that the same 4$π$ quantum anomaly occurs when bridging two spinless Thouless pumps to a p-wave superconducting region that could be as small as a single and experimentally-relevant superconducting quantum dot - a point-like defect. This interpretation as a dual Josephson effect never requires the presence of Majorana modes but rather builds on the topological properties of adiabatic quantum pumps with Z topological invariants. It allows for the systematic construction of dual Josephson effects of arbitrary periodicity, such as 4$π$ and 8$π$, by using point-like defects whose symmetry differs from that of the pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically discussed via mappings to two-dimensional geometries, we show that this phenomenology does not have any counterpart in conventional two-dimensional systems. △ Less

Submitted 10 January, 2019; originally announced January 2019.

Journal ref: Phys. Rev. B 99, 125153 (2019)

Stabilizing arrays of photonic cat states via spontaneous symmetry breaking

Authors: José Lebreuilly, Camille Aron, Christophe Mora

Abstract: The controlled generation and the protection of entanglement is key to quantum simulation and quantum computation. At the single-mode level, protocols based on photonic cat states hold strong promise as they present unprecedentedly long-lived coherence and may be combined with powerful error correction schemes. Here, we demonstrate that robust ensembles of "many-body photonic cat states" can be ge… ▽ More The controlled generation and the protection of entanglement is key to quantum simulation and quantum computation. At the single-mode level, protocols based on photonic cat states hold strong promise as they present unprecedentedly long-lived coherence and may be combined with powerful error correction schemes. Here, we demonstrate that robust ensembles of "many-body photonic cat states" can be generated in a Bose-Hubbard model with pair hopping via a spontaneous U(1) symmetry breaking mechanism. We identify a parameter region where the ground state is a massively degenerate manifold consisting of local cat states which are factorized throughout the lattice and whose conserved individual parities can be used to make a register of qubits. This phenomenology occurs for arbitrary system sizes or geometries, as soon as long-range order is established, and it extends to driven-dissipative conditions. In the thermodynamic limit, it is related to a Mott insulator to pair-superfluid phase transition. △ Less

Submitted 6 March, 2019; v1 submitted 27 September, 2018; originally announced September 2018.

Journal ref: Phys. Rev. Lett. 122, 120402 (2019)

Bipartite Fluctuations and Topology of Dirac and Weyl Systems

Authors: Loïc Herviou, Karyn Le Hur, Christophe Mora

Abstract: Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the Quantum Fisher information. Through the example of t… ▽ More Bipartite fluctuations can provide interesting information about entanglement properties and correlations in many-body quantum systems. We address such fluctuations in relation with the topology of Dirac and Weyl quantum systems, in situations where the relevant particle number is not conserved, leading to additional volume laws scaling with the Quantum Fisher information. Through the example of the $p+ip$ superconductor, we build a relation between charge fluctuations and the associated winding numbers of Dirac cones in the low-energy sector. Topological aspects of the Hamiltonian in the vicinity of these points induce long-range entanglement in real space. We provide a detailed analysis of such fluctuation properties, including the role of gap anisotropy, and discuss higher-dimensional Weyl analogues. △ Less

Submitted 21 September, 2018; originally announced September 2018.

Comments: 21 pages, incl. 5 of Appendices. All comments welcome

Journal ref: Phys. Rev. B 99, 075133 (2019)

Braiding Majorana zero modes using quantum dots

Authors: Corneliu Malciu, Leonardo Mazza, Christophe Mora

Abstract: We discuss a network of Kitaev wires coupled to several individually-tunable quantum dots as an extension of the recent experiments on a quantum dot coupled to a nanowire hosting Majorana zero modes [Deng et al. Science 354 1557 (2016) and Deng et al. arXiv:1712.03536 (2017)]. The setup features localized Majorana modes with exact zero energy and we show that they can be manipulated by solely acti… ▽ More We discuss a network of Kitaev wires coupled to several individually-tunable quantum dots as an extension of the recent experiments on a quantum dot coupled to a nanowire hosting Majorana zero modes [Deng et al. Science 354 1557 (2016) and Deng et al. arXiv:1712.03536 (2017)]. The setup features localized Majorana modes with exact zero energy and we show that they can be manipulated by solely acting on the quantum dots. A braiding process can be obtained by arranging three wires as a trijunction and a charge readout of the quantum dots can be used to reveal the non-Abelian statistics of Majorana zero modes. The setup can be scaled up to serve the more advanced purposes of topological quantum computation. △ Less

Submitted 23 May, 2018; originally announced May 2018.

Comments: 14 pages, 10 figures

Journal ref: Phys. Rev. B 98, 165426 (2018)

Parametric amplification and squeezing with an ac- and dc-voltage biased superconducting junction

Authors: Udson C. Mendes, Sébastien Jezouin, Philippe Joyez, Bertrand Reulet, Alexandre Blais, Fabien Portier, Christophe Mora, Carles Altimiras

Abstract: We theoretically investigate a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction. Photon-assisted tunneling, resulting from the combination of dc- and ac-voltage bias, gives rise to a strong parametric interaction for the electromagnetic modes reflected by the junction coupled to a transm… ▽ More We theoretically investigate a near-quantum-limited parametric amplifier based on the nonlinear dynamics of quasiparticles flowing through a superconducting-insulator-superconducting junction. Photon-assisted tunneling, resulting from the combination of dc- and ac-voltage bias, gives rise to a strong parametric interaction for the electromagnetic modes reflected by the junction coupled to a transmission line. We show phase-sensitive and phase-preserving amplification, together with single- and two-mode squeezing. For an aluminum junction pumped at twice the center frequency, $ω_0/2π=6$~GHz, we predict narrow-band phase-sensitive amplification of microwaves signals to more than 20 dB, and broadband phase-preserving amplification of 20 dB over a 1.2 GHz 3-dB bandwidth. We also predict single- and two-mode squeezing reaching more than -12 dB over 5.3 GHz 3-dB bandwidth. Moreover, with a simple impedance matching circuit, we demonstrate 3 dB bandwidth reaching 4.3 GHz for 20 dB of gain. A key feature of the device is that its performance can be controlled in-situ with the applied dc- and ac-voltage biases. △ Less

Submitted 6 March, 2019; v1 submitted 20 February, 2018; originally announced February 2018.

Comments: Accepted for publication at the Physical Review Applied. 12 pages and 9 figures

Journal ref: Phys. Rev. Applied 11, 034035 (2019)

Two-color Fermi liquid theory for transport through a multilevel Kondo impurity

Authors: D. B. Karki, Christophe Mora, Jan von Delft, Mikhail N. Kiselev

Abstract: We consider a quantum dot with ${\cal K}{\geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we de… ▽ More We consider a quantum dot with ${\cal K}{\geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries. △ Less

Submitted 27 March, 2018; v1 submitted 1 February, 2018; originally announced February 2018.

Comments: 16 pages, 13 figures

Journal ref: Phys. Rev. B 97, 195403 (2018)

Non-topological parafermions in a one-dimensional fermionic model with even multiplet pairing

Authors: Leonardo Mazza, Fernando Iemini, Marcello Dalmonte, Christophe Mora

Abstract: We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-fold degenerate ground state robust to certain disorder. In… ▽ More We discuss a one-dimensional fermionic model with a generalized $\mathbb{Z}_{N}$ even multiplet pairing extending Kitaev $\mathbb{Z}_{2}$ chain. The system shares many features with models believed to host localized edge parafermions, the most prominent being a similar bosonized Hamiltonian and a $\mathbb{Z}_{N}$ symmetry enforcing an $N$-fold degenerate ground state robust to certain disorder. Interestingly, we show that the system supports a pair of parafermions but they are non-local instead of being boundary operators. As a result, the degeneracy of the ground state is only partly topological and coexists with spontaneous symmetry breaking by a (two-particle) pairing field. Each symmetry-breaking sector is shown to possess a pair of Majorana edge modes encoding the topological twofold degeneracy. Surrounded by two band insulators, the model exhibits for $N=4$ the dual of an $8 π$ fractional Josephson effect highlighting the presence of parafermions. △ Less

Submitted 16 November, 2018; v1 submitted 25 January, 2018; originally announced January 2018.

Comments: 12 pages, 3 figures

Journal ref: Phys. Rev. B 98, 201109 (2018)

Tunable Quantum Criticality and Super-ballistic Transport in a `Charge' Kondo Circuit

Authors: Z. Iftikhar, A. Anthore, A. K. Mitchell, F. D. Parmentier, U. Gennser, A. Ouerghi, A. Cavanna, C. Mora, P. Simon, F. Pierre

Abstract: Quantum phase transitions are ubiquitous in many exotic behaviors of strongly-correlated materials. However the microscopic complexity impedes their quantitative understanding. Here, we observe thoroughly and comprehend the rich strongly-correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model,… ▽ More Quantum phase transitions are ubiquitous in many exotic behaviors of strongly-correlated materials. However the microscopic complexity impedes their quantitative understanding. Here, we observe thoroughly and comprehend the rich strongly-correlated physics in two profoundly dissimilar regimes of quantum criticality. With a circuit implementing a quantum simulator for the three-channel Kondo model, we reveal the universal scalings toward different low-temperature fixed points and along the multiple crossovers from quantum criticality. Notably, an unanticipated violation of the maximum conductance for ballistic free electrons is uncovered. The present charge pseudospin implementation of a Kondo impurity opens access to a broad variety of strongly-correlated phenomena. △ Less

Submitted 3 July, 2018; v1 submitted 8 August, 2017; originally announced August 2017.

Comments: Article (6 figures) with supplementary (4 figures); http://science.sciencemag.org/content/360/6395/1315

Journal ref: Science 360, 1315-1320 (2018)

Driven dissipative dynamics and topology of quantum impurity systems

Authors: Karyn Le Hur, Loïc Henriet, Loïc Herviou, Kirill Plekhanov, Alexandru Petrescu, Tal Goren, Marco Schiro, Christophe Mora, Peter P. Orth

Abstract: In this review, we provide an introduction and overview to some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin-boson and related models, which describes a single spin-1/2 coupled to an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we als… ▽ More In this review, we provide an introduction and overview to some more recent advances in real-time dynamics of quantum impurity models and their realizations in quantum devices. We focus on the Ohmic spin-boson and related models, which describes a single spin-1/2 coupled to an infinite collection of harmonic oscillators. The topics are largely drawn from our efforts over the past years, but we also present a few novel results. In the first part of this review, we begin with a pedagogical introduction to the real-time dynamics of a dissipative spin at both high and low temperatures. We then focus on the driven dynamics in the quantum regime beyond the limit of weak spin-bath coupling. In these situations, the non-perturbative stochastic Schroedinger equation method is ideally suited to numerically obtain the spin dynamics as it can incorporate bias fields $h_z(t)$ of arbitrary time-dependence in the Hamiltonian. We present different recent applications of this method: (i) how topological properties of the spin such as the Berry curvature and the Chern number can be measured dynamically, and how dissipation affects the topology and the measurement protocol, (ii) how quantum spin chains can experience synchronization dynamics via coupling to a common bath. In the second part of this review, we discuss quantum engineering of spin-boson and related models in circuit quantum electrodynamics (cQED), quantum electrical circuits and cold-atoms architectures. In different realizations, the Ohmic environment can be represented by a long (microwave) transmission line, a Luttinger liquid, a one-dimensional Bose-Einstein condensate, a chain of superconducting Josephson junctions. We show that the quantum impurity can be used as a quantum sensor to detect properties of a bath at minimal coupling, and how dissipative spin dynamics can lead to new insight in the Mott-Superfluid transition. △ Less

Submitted 20 July, 2018; v1 submitted 16 February, 2017; originally announced February 2017.

Comments: 39 pages, invited review, Comptes Rendus Académie des Sciences, Special Issue on Quantum Simulators, Version as published

Bipartite charge fluctuations in one-dimensional $\mathbb{Z}_2$ superconductors and insulators

Authors: Loic Herviou, Christophe Mora, Karyn Le Hur

Abstract: Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems). In this Letter, we study the BCF in generic one-dimensional… ▽ More Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems). In this Letter, we study the BCF in generic one-dimensional $\mathbb{Z}_2$ (topological) models including the Kitaev superconducting wire model, the Ising chain or various topological insulators such as the SSH model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the XYZ model. △ Less

Submitted 13 February, 2017; originally announced February 2017.

Comments: 6 pages + Supp Mat (6 pages), to be submitted, all comments are welcomed

Journal ref: Phys. Rev. B 96, 121113 (2017)

Noise of a chargeless Fermi liquid

Authors: Catalin Pascu Moca, Christophe Mora, Ireneusz Weymann, Gergely Zarand

Abstract: We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot- normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudo-charge.… ▽ More We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot- normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudo-charge. In contrast to other correlated Fermi-liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, $e^* = 2e$. In addition,we find a strong suppression of noise when the linear conductance is unitary, even for its non-linear part. △ Less

Submitted 22 January, 2017; originally announced January 2017.

Comments: 5 pages, 4 figures and 5 pages of supplementary material with 3 figures

Journal ref: Phys. Rev. Lett. 120, 016803 (2018)

Topological phases of parafermions: a model with exactly-solvable ground states

Authors: Fernando Iemini, Christophe Mora, Leonardo Mazza

Abstract: Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave-functions, which are matrix-product states and have a particularly elegant interpretation in terms of Fock parafer… ▽ More Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave-functions, which are matrix-product states and have a particularly elegant interpretation in terms of Fock parafermions, reflecting the factorized nature of the ground states. Using these wavefunctions, we demonstrate analytically several signatures of topological order. Our study provides a starting point for the non-approximate study of topological one-dimensional parafermionic chains with spatial-inversion and time-reversal symmetry in the absence of strong edge modes. △ Less

Submitted 11 April, 2017; v1 submitted 2 November, 2016; originally announced November 2016.

Comments: 6 + 9 pages, 3 figures

Journal ref: Phys. Rev. Lett. 118, 170402 (2017)

At which magnetic field, exactly, does the Kondo resonance begin to split? A Fermi liquid description of the low-energy properties of the Anderson model

Authors: Michele Filippone, Catalin Pascu Moca, Andreas Weichselbaum, Jan von Delft, Christophe Mora

Abstract: This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora $et al.$, Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To descr… ▽ More This paper is a corrected version of Phys. Rev. B 95, 165404 (2017), which we have retracted because it contained a trivial but fatal sign error that lead to incorrect conclusions. --- We extend a recently-eveloped Fermi-liquid (FL) theory for the asymmetric single-impurity Anderson model [C. Mora $et al.$, Phys. Rev. B, 92, 075120 (2015)] to the case of an arbitrary local magnetic field. To describe the system's low-lying quasiparticle excitations for arbitrary values of the bare Hamiltonian's model parameters, we construct an effective low-energy FL Hamiltonian whose FL parameters are expressed in terms of the local level's spin-dependent ground-state occupations and their derivatives with respect to level energy and local magnetic field. These quantities are calculable with excellent accuracy from the Bethe Ansatz solution of the Anderson model. Applying this effective model to a quantum dot in a nonequilibrium setting, we obtain exact results for the curvature of the spectral function, $c_A$, describing its leading $\sim\varepsilon^2$ term, and the transport coefficients $c_V$ and $c_T$, describing the leading $\sim V^2$ and $\sim T^2$ terms in the nonlinear differential conductance. A sign change in $c_A$ or $c_V$ is indicative of a change from a local maximum to a local minimum in the spectral function or nonlinear conductance, respectively, as is expected to occur when an increasing magnetic field causes the Kondo resonance to split into two subpeaks. We find that the fields $B_A$, $B_T$ and $B_V$ at which $c_A$, $c_T$ and $c_V$ change sign, respectively, are all of order $T_K$, as expected, with $B_A = B_T = B_V = 0.75073\,T_K$ in the Kondo limit. △ Less

Submitted 17 July, 2018; v1 submitted 20 September, 2016; originally announced September 2016.

Comments: 21 pages, 18 figures. Version 1 of this paper, published as Phys. Rev. B 95, 165404 (2017), contained a trivial but fatal sign error that lead to incorrect physical conclusions; it has therefore been retracted. Version 3 is a corrected version with major revisions, additional NRG data and different conclusions; it has been accepted for publication in PRB

Journal ref: Phys. Rev. B 98, 075404 (2018)

Many-terminal Majorana island: from Topological to Multi-Channel Kondo Model

Authors: Loïc Herviou, Karyn Le Hur, Christophe Mora

Abstract: We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multi-channel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a… ▽ More We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multi-channel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter $K$ in the leads that is effectively doubled. For strong interaction, $K=1/2$, the intermediate fixed point of the standard multi-channel Kondo model is exactly recovered. It evolves with $K$ and connects to strong coupling in non-interacting case $K=1$, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multi-channel Kondo state. △ Less

Submitted 15 September, 2016; v1 submitted 14 September, 2016; originally announced September 2016.

Comments: 15 pages, 3 figures, to be submitted to PRB - figure compilation solved

Journal ref: Phys. Rev. B 94, 235102 (2016)

Electron-photon interaction in a quantum point contact coupled to a microwave resonator

Authors: Udson C. Mendes, Christophe Mora

Abstract: We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and… ▽ More We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and pair absorption dominates over pair emission for all bias voltages. As a result, the number of cavity photons, the cavity damping rate and the second order coherence $g^{(2)}$ are all reduced and exhibit less bunching than the thermal state. These results are obtained with a Keldysh path integral formulation and reproduced with rate equations. They can be seen as a backaction of the cavity measuring the electronic noise. Extending the standard $P(E)$ theory to a steady-state situation, we compute the modified noise properties of the conductor and find quantitative agreement with the perturbative calculation. △ Less

Submitted 13 April, 2016; originally announced April 2016.

Comments: 16 pages, 4 figures

Journal ref: Phys. Rev. B 93, 235450 (2016)

Phase Diagram and Entanglement of two interacting topological Kitaev chains

Authors: Loïc Herviou, Christophe Mora, Karyn Le Hur

Abstract: A superconducting wire described by a p-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moder… ▽ More A superconducting wire described by a p-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultra-cold atoms and Josephson junctions. △ Less

Submitted 3 April, 2016; v1 submitted 12 January, 2016; originally announced January 2016.

Comments: Final Version to be Published in Phys. Rev. B; 24 pages and 15 figures

Journal ref: Phys. Rev. B 93, 165142 (2016)

Quantum Properties of the radiation emitted by a conductor in the Coulomb Blockade Regime

Authors: Christophe Mora, Carles Altimiras, Philippe Joyez, Fabien Portier

Abstract: We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the non-linearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the… ▽ More We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the non-linearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the interaction between a quantum conductor and electromagnetic fields can be exploited as a resource to design simple sources of non-classical radiation. △ Less

Submitted 28 March, 2017; v1 submitted 17 December, 2015; originally announced December 2015.

Comments: 14 pages, 4 figures, includes Supplementary

Journal ref: Phys. Rev. B 95, 125311 (2017)

Cavity quantum electrodynamics with an out-of-equilibrium quantum dot

Authors: Olesia Dmytruk, Mircea Trif, Christophe Mora, Pascal Simon

Abstract: We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in details how the measurements of the cavity microwave field, which are related to the electronic charge susceptibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive coupli… ▽ More We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in details how the measurements of the cavity microwave field, which are related to the electronic charge susceptibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive couplings between the electronic reservoirs and the cavity plays a crucial role in relating optical measurements to transport properties. For asymmetric capacitive couplings, photonic measurements can be used to probe the finite low frequency admittance of the quantum conductor, the real part of which being related to the differential conductance. In particular, when the quantum dot is far from resonance, the charge susceptibility is directly proportional to the admittance for a large range of frequencies and voltages. However, when the quantum conductor is near a resonance, such a relation generally holds only at low frequency and for equal tunnel coupling or low voltage. Beyond this low-energy near equilibrium regime, the charge susceptibility and thus the optical transmission offers new insights on the quantum conductors since the optical observables are not directly connected to transport quantities. For symmetric lead capacitive couplings, we show that the optical measurements can be used to reveal the Korringa-Shiba relation, connecting the reactive to the dissipative part of the susceptibility, at low frequency and low bias. △ Less

Submitted 16 February, 2016; v1 submitted 13 October, 2015; originally announced October 2015.

Comments: 16 pages, 6 figures, published version

Journal ref: Phys. Rev. B 93, 075425 (2016)

Cavity squeezing by a quantum conductor

Authors: Udson C. Mendes, Christophe Mora

Abstract: Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron-photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squ… ▽ More Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron-photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squeezed steady state in the cavity. We find that squeezing properties of the cavity are essentially determined by the electronic noise correlators of the quantum conductor. In the case of a tunnel junction, we predict that squeezing is optimized by applying a time-periodic series of quantized $δ-$peaks in the bias voltage. For an asymmetric quantum dot, we show that a sharp Leviton pulse is able to achieve perfect cavity squeezing. △ Less

Submitted 6 November, 2015; v1 submitted 30 April, 2015; originally announced May 2015.

Comments: 13 pages, 4 figures, includes Supplementary info

Journal ref: New J. Phys. 17, 113014 (2015)