Showing 1–50 of 188 results for author: Stern, A

Probing chiral topological states with permutation defects

Authors: Yarden Sheffer, Ruihua Fan, Ady Stern, Erez Berg, Shinsei Ryu

Abstract: The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wavefunction itself remains only partially understood. In this work, we introduce a family of multipartite entanglement measures that probe chirality directly from the bulk wavefunction. Our construct… ▽ More The hallmark of two-dimensional chiral topological phases is the existence of anomalous gapless modes at the spatial boundary. Yet, the manifestation of this edge anomaly within the bulk ground-state wavefunction itself remains only partially understood. In this work, we introduce a family of multipartite entanglement measures that probe chirality directly from the bulk wavefunction. Our construction involves applying different permutations between replicas of the ground state wavefunction in neighboring spatial regions, creating "permutation defects" at the boundaries between these regions. We provide general arguments for the robustness of these measures and develop a field-theoretical framework to compute them systematically. While the standard topological field theory prescription misses the chiral contribution, our method correctly identifies it as the chiral conformal field theory partition function on high-genus Riemann surfaces. This feature is a consequence of the bulk-edge correspondence, which dictates that any regularization of the theory at the permutation defects must introduce gapless boundary modes. We numerically verify our results with both free-fermion and strongly-interacting chiral topological states and find excellent agreement. Our results enable the extraction of the chiral central charge and the Hall conductance using a finite number of wavefunction replicas, making these quantities accessible to Monte-Carlo numerical techniques and noisy intermediate-scale quantum devices. △ Less

Submitted 4 December, 2025; originally announced December 2025.

Comments: 16+14 pages, 20 figures, comments welcome!

Momentum-Resolved Spectroscopy of Superconductivity with the Quantum Twisting Microscope

Authors: Yuval Waschitz, Ady Stern, Yuval Oreg

Abstract: We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Due to in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative in… ▽ More We develop a theoretical framework for probing superconductivity with momentum resolution using the quantum twisting microscope (QTM), a planar tunneling device where a graphene tip is rotated relative to a two-dimensional sample. Due to in-plane momentum conservation, the QTM directly measures the superconducting spectral function along well-defined trajectories in momentum space. The relative intensities of electron and hole excitations encode the Bogoliubov coherence factors, revealing the momentum dependence of the pairing magnitude. Three $C_{3z}$-related tunneling channels enable direct detection of rotational symmetry breaking, as well as nodal points in the superconducting order parameter. We apply our framework to superconductivity within the Bistritzer-MacDonald model of noninteracting electrons and the Topological Heavy Fermion model, which accounts for electron-electron interactions. Together, these capabilities establish the QTM as a direct probe of the pairing symmetry and microscopic origin of superconductivity in two-dimensional materials. △ Less

Submitted 15 October, 2025; originally announced October 2025.

Comments: 24 pages, 12 figures

Topological phase transitions between bosonic and fermionic quantum Hall states near even-denominator filling factors

Authors: Evgenii Zheltonozhskii, Ady Stern, Netanel H. Lindner

Abstract: We study the quantum critical point between the fermionic $ν=8$ quantum Hall state and the bosonic $ν=2$ quantum Hall state of Cooper pairs. Our study is motivated by the composite fermion construction for the daughter states of even-denominator fractional quantum Hall states and the experimentally observed transition between the daughter and the Jain states at the same filling. We show that this… ▽ More We study the quantum critical point between the fermionic $ν=8$ quantum Hall state and the bosonic $ν=2$ quantum Hall state of Cooper pairs. Our study is motivated by the composite fermion construction for the daughter states of even-denominator fractional quantum Hall states and the experimentally observed transition between the daughter and the Jain states at the same filling. We show that this transition is equivalent to the transition between a neutral invertible $E_8$ state and a topologically trivial state. These transitions can be described in a partonic framework as a cascade of mass changes of four neutral Dirac fermions coupled to multiple Abelian Chern-Simons $U(1)$ gauge fields. In the absence of fine-tuning, the transition is split into a series of four or more different transitions, with at least three distinct intermediate topologically ordered phases hosting neutral anyons. △ Less

Submitted 24 August, 2025; originally announced August 2025.

Gapfull and gapless $1$D Topological Superconductivity in Spin-Orbit Coupled Bilayer Graphene

Authors: Daniel Skliannyi, Yuval Oreg, Ady Stern

Abstract: We propose a way to generate a one-dimensional topological superconductor from a monolayer of a transition metal dichalcogenide coupled to a Bernal-stacked bilayer of graphene under a displacement field. With proper gating, this structure may be tuned to form three parallel pads of superconductors creating two planar Josephson junctions in series, in which normal regions separate the superconducto… ▽ More We propose a way to generate a one-dimensional topological superconductor from a monolayer of a transition metal dichalcogenide coupled to a Bernal-stacked bilayer of graphene under a displacement field. With proper gating, this structure may be tuned to form three parallel pads of superconductors creating two planar Josephson junctions in series, in which normal regions separate the superconductors. Two characteristics of the system which are essential for our discussion are spin orbit coupling induced by the transition metal dichalcogenides and the variation of the Fermi velocities along the Fermi surface. We demonstrate that these two characteristics lead to one-dimensional topological superconductivity occupying large parts in the parameter space defined by the two phase differences across the two junctions and the relative angle between the junctions and the lattice. An angle-shaped device in which this angle varies in space, combined with proper phase tuning, can lead to the formation of domain walls between topological and trivial phases, supporting a zero-energy Majorana mode, within the bulk of carefully designed devices. We derive the spectrum of the Andreev bound states and show that Ising spin-orbit coupling leaves the topological superconductor gapless, and the Rashba spin-orbit coupling opens a gap in its spectrum. Our analysis shows that the transition to a gapped topological state is a result of the band inversion of Andreev states. △ Less

Submitted 2 October, 2025; v1 submitted 22 April, 2025; originally announced April 2025.

Journal ref: Phys. Rev. B 112, 134504 (2025)

Flux attachment theory of fractional excitonic insulators

Authors: Steven Gassner, Ady Stern, C. L. Kane

Abstract: The search for fractional quantized Hall phases in the absence of a magnetic field has primarily targeted flat-band systems that mimic the features of a Landau level. In an alternative approach, the fractional excitonic insulator (FEI) has been proposed as a correlated electron-hole fluid that arises near a band inversion between bands of different angular momentum with strong interactions. It rem… ▽ More The search for fractional quantized Hall phases in the absence of a magnetic field has primarily targeted flat-band systems that mimic the features of a Landau level. In an alternative approach, the fractional excitonic insulator (FEI) has been proposed as a correlated electron-hole fluid that arises near a band inversion between bands of different angular momentum with strong interactions. It remains an interesting challenge to find Hamiltonians with realistic interactions that stabilize this state. Here, we describe composite boson and composite fermion theories that highlight the importance of $(p_x+ip_y)^m$ excitonic pairing in stabilizing FEIs in a class of band inversion models. We predict a sequence of Jain-like and Laughlin-like FEI states, the simplest of which has the topological order of the bosonic $ν=1/2$ fractional quantized Hall state. We discuss implications for recent numerical studies on a chiral spin liquid phase in interacting Chern insulator models. △ Less

Submitted 30 October, 2025; v1 submitted 7 April, 2025; originally announced April 2025.

Journal ref: Phys. Rev. Lett. 135, 186602 (2025)

Concurrent Multifractality and Anomalous Hall Response in the Nodal Line Semimetal Fe$_3$GeTe$_2$ Near Localization

Authors: Subramanian Mathimalar, Ambikesh Gupta, Yotam Roet, Stanislaw Galeski, Rafal Wawrzynczak, Mikel Garcia-Diez, Iñigo Robredo, Praveen Vir, Nitesh Kumar, Walter Schnelle, Karin von Arx, Julia Küspert, Qisi Wang, Johan Chang, Yasmine Sassa, Ady Stern, Felix von Oppen, Maia G. Vergniory, Claudia Felser, Johannes Gooth, Nurit Avraham, Haim Beidenkopf

Abstract: Topological states of matter exhibit unique protection against scattering by disorder. Different topological classes exhibit distinct forms and degrees of protection. Here, we investigate the response of the ferromagnetic nodal line semimetal Fe$_3$GeTe$_2$ to disorder and electronic interactions. By combining global magneto-transport with atomic-scale scanning tunneling spectroscopy we find a sim… ▽ More Topological states of matter exhibit unique protection against scattering by disorder. Different topological classes exhibit distinct forms and degrees of protection. Here, we investigate the response of the ferromagnetic nodal line semimetal Fe$_3$GeTe$_2$ to disorder and electronic interactions. By combining global magneto-transport with atomic-scale scanning tunneling spectroscopy we find a simultaneous onset of diverse phenomena below a common temperature scale of about 15 K: A crossover from metallic to insulating temperature dependence of the longitudinal resistivity, saturation of the anomalous Hall conductivity to its maximal value, formation of a sharp zero-bias dip in the tunneling density of state, and emergence of multi-fractal structure of the electronic wavefunction peaking at the Fermi energy. These concurrent observations reflect the emergence of a novel energy scale possibly related to the opening of a gap in the nodal line band of Fe$_3$GeTe$_2$. Our study provides overarching insight into the role of disorder, electronic interactions and Berry curvature in setting the micro- and macro-scale responses of topological semimetals. △ Less

Submitted 6 March, 2025; originally announced March 2025.

Extracting topological spins from bulk multipartite entanglement

Authors: Yarden Sheffer, Ady Stern, Erez Berg

Abstract: We address the problem of identifying a 2+1d topologically ordered phase using measurements on the ground-state wavefunction. For non-chiral topological order, we describe a series of bulk multipartite entanglement measures that extract the invariants $\sum_a d_a^2 θ_a^r$ for any $r \geq 2$, where $d_a$ and $θ_a$ are the quantum dimension and topological spin of an anyon $a$, respectively. These i… ▽ More We address the problem of identifying a 2+1d topologically ordered phase using measurements on the ground-state wavefunction. For non-chiral topological order, we describe a series of bulk multipartite entanglement measures that extract the invariants $\sum_a d_a^2 θ_a^r$ for any $r \geq 2$, where $d_a$ and $θ_a$ are the quantum dimension and topological spin of an anyon $a$, respectively. These invariants are obtained as expectation values of permutation operators between $2r$ replicas of the wavefunction, applying different permutations on four distinct regions of the plane. Our proposed measures provide a refined tool for distinguishing topological phases, capturing information beyond conventional entanglement measures such as the topological entanglement entropy. We argue that any operator capable of extracting the above invariants must act on at least $2r$ replicas, making our procedure optimal in terms of the required number of replicas. We discuss the generalization of our results to chiral states. △ Less

Submitted 24 July, 2025; v1 submitted 17 February, 2025; originally announced February 2025.

Comments: Accepted to PRL, 6+7 pages, 6 figures, comments welcome

Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States

Authors: Jehyun Kim, Himanshu Dev, Amit Shaer, Ravi Kumar, Alexey Ilin, André Haug, Shelly Iskoz, Kenji Watanabe, Takashi Taniguchi, David F. Mross, Ady Stern, Yuval Ronen

Abstract: Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically-protected way. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments. In this work, we present the observation of coherent Aharonov-Bohm interference at two even… ▽ More Position exchange of non-Abelian anyons affects the quantum state of their system in a topologically-protected way. Their expected manifestations in even-denominator fractional quantum Hall (FQH) systems offer the opportunity to directly study their unique statistical properties in interference experiments. In this work, we present the observation of coherent Aharonov-Bohm interference at two even-denominator states in high-mobility bilayer graphene-based van der Waals heterostructures by employing the Fabry-Pérot interferometry (FPI) technique. Operating the interferometer at a constant filling factor, we observe an oscillation period corresponding to two flux quanta inside the interference loop, $ΔΦ=2Φ_0$, at which the interference does not carry signatures of non-Abelian statistics. The absence of the expected periodicity of $ΔΦ=4Φ_0$ may indicate that the interfering quasiparticles carry the charge $e^* = \frac{1}{2}e$ or that interference of $e^* = \frac{1}{4}e$ quasiparticles is thermally smeared. Interestingly, at two hole-conjugate states, we also observe oscillation periods of half the expected value, indicating interference of $e^* = \frac{2}{3}e$ quasiparticles instead of $e^* = \frac{1}{3}e$. To probe statistical phase contributions, we operated the FPI with controlled deviations of the filling factor, thereby introducing fractional quasiparticles inside the interference loop. The resulting changes to the interference patterns at both half-filled states indicate that the additional bulk quasiparticles carry the fundamental charge $e^*=\frac{1}{4}e$, as expected for non-Abelian anyons. △ Less

Submitted 27 December, 2024; originally announced December 2024.

Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces

Authors: Misha Yutushui, Ady Stern, David F. Mross

Abstract: Multiple topologically distinct quantum Hall phases can occur at the same Landau level filling factor. It is a major challenge to distinguish between these phases as they only differ by the neutral modes, which do not affect the charge conductance in conventional geometries. We show that the neutral sector can be determined with coherent charge conductance in a $π$-shaped geometry that interfaces… ▽ More Multiple topologically distinct quantum Hall phases can occur at the same Landau level filling factor. It is a major challenge to distinguish between these phases as they only differ by the neutral modes, which do not affect the charge conductance in conventional geometries. We show that the neutral sector can be determined with coherent charge conductance in a $π$-shaped geometry that interfaces three different filling factors. Specifically, non-Abelian paired states at a half-filled Landau level and the anti-Read-Rezayi state can be identified. Interestingly, for interfaces between paired states and Jain states, the electric current in the $π$ geometry behaves as if pairs of neutral Majoranas edge modes were charge modes of Jain states. △ Less

Submitted 11 December, 2024; originally announced December 2024.

Comments: 4+8 page, 3+1 figures, 2 tables

Journal ref: Phys. Rev. Lett. 134, 206301, (2025)

Preparing topological states with finite depth simultaneous commuting gates

Authors: Yarden Sheffer, Erez Berg, Ady Stern

Abstract: We present protocols for preparing two-dimensional abelian and non-abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols are motivated by recent proposals for circuits in trapped ion systems, which allow each qubit to participate in multiple gates simultaneously. Our circuits are… ▽ More We present protocols for preparing two-dimensional abelian and non-abelian topologically ordered states by employing finite depth unitary circuits composed of long-ranged, simultaneous, and mutually commuting two-qubit gates. Our protocols are motivated by recent proposals for circuits in trapped ion systems, which allow each qubit to participate in multiple gates simultaneously. Our circuits are shown to be optimal, in the sense that the number of two-qubit gates and ancilla qubits scales as $O(L^2)$, where $L$ is the linear size of the system. Examples include the ground states of the toric code, certain Kitaev quantum double models, and string net models. Going beyond two dimensions, we extend our scheme to more general Calderbank-Shor-Steane (CSS) codes. As an application, we present protocols for realizing the three-dimensional Haah's code and X-Cube fracton models. △ Less

Submitted 15 October, 2024; originally announced October 2024.

Comments: 15 pages, 9 figures

Strongly interacting Hofstadter states in magic-angle twisted bilayer graphene

Authors: Minhao He, Xiaoyu Wang, Jiaqi Cai, Jonah Herzog-Arbeitman, Takashi Taniguchi, Kenji Watanabe, Ady Stern, B. Andrei Bernevig, Matthew Yankowitz, Oskar Vafek, Xiaodong Xu

Abstract: Magic-angle twisted bilayer graphene (MATBG) hosts a multitude of strongly correlated states at partial fillings of its flat bands. In a magnetic field, these flat bands further evolve into a unique Hofstadter spectrum renormalized by strong Coulomb interactions. Here, we study the interacting Hofstadter states spontaneously formed within the topological magnetic subbands of an ultraclean MATBG de… ▽ More Magic-angle twisted bilayer graphene (MATBG) hosts a multitude of strongly correlated states at partial fillings of its flat bands. In a magnetic field, these flat bands further evolve into a unique Hofstadter spectrum renormalized by strong Coulomb interactions. Here, we study the interacting Hofstadter states spontaneously formed within the topological magnetic subbands of an ultraclean MATBG device, notably including symmetry-broken Chern insulator (SBCI) states and fractional quantum Hall (FQH) states. The observed SBCI states form a cascade with their Chern numbers mimicking the main sequence correlated Chern insulators. The FQH states in MATBG form in Jain sequence; however, they disappear at high magnetic field, distinct from conventional FQH states which strengthen with increasing magnetic field. We reveal a unique magnetic field-driven phase transition from composite fermion phases to a dissipative Fermi liquid. Our theoretical analysis of the magnetic subbands hosting FQH states predicts non uniform quantum geometric properties far from the lowest Landau level. This points towards a more natural interpretation of these FQH states as in-field fractional Chern insulators of the magnetic subbands. △ Less

Submitted 2 August, 2024; originally announced August 2024.

Realizing string-net condensation: Fibonacci anyon braiding for universal gates and sampling chromatic polynomials

Authors: Zlatko K. Minev, Khadijeh Najafi, Swarnadeep Majumder, Juven Wang, Ady Stern, Eun-Ah Kim, Chao-Ming Jian, Guanyu Zhu

Abstract: The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this complexity use the Fibonacci string-net condensate (Fib-SNC) and its Fibonacci anyons to go beyond classical computing. Sampling the Fib-SNC wavefunction is expe… ▽ More The remarkable complexity of the vacuum state of a topologically-ordered many-body quantum system encodes the character and intricate braiding interactions of its emergent particles, the anyons.} Quintessential predictions exploiting this complexity use the Fibonacci string-net condensate (Fib-SNC) and its Fibonacci anyons to go beyond classical computing. Sampling the Fib-SNC wavefunction is expected to yield estimates of the chromatic polynomial of graph objects, a classical task that is provably hard. At the same time, exchanging anyons of Fib-SNC is expected to allow fault-tolerant universal quantum computation. Nevertheless, the physical realization of Fib-SNC and its anyons remains elusive. Here, we introduce a scalable dynamical string-net preparation (DSNP) approach, suitable even for near-term quantum processors, which dynamically prepares Fib-SNC and its anyons through reconfigurable graphs. Using a superconducting quantum processor, we couple the DSNP approach with composite error-mitigation on deep circuits to successfully create, measure, and braid anyons of Fib-SNC in a scalable manner. We certify the creation of anyons by measuring their `anyon charge', finding an average experimental accuracy of $94\%$. Furthermore, we validate that exchanging these anyons yields the { expected} golden ratio~$φ$ with~$98\%$ average accuracy and~$8\%$ measurement uncertainty. Finally, we sample the Fib-SNC to estimate the chromatic polynomial at~$φ+2$ for {several} graphs. Our results establish the proof of principle for using Fib-SNC and its anyons for fault-tolerant universal quantum computation and {for aiming at} a classically-hard problem. △ Less

Submitted 11 April, 2025; v1 submitted 18 June, 2024; originally announced June 2024.

Comments: 4 pages and 4 figures with Supplemental Materials (49 pages, 20 Figures)

Journal ref: Nature Communications 16, 6225 (2025)

Electronic Excitations in the Bulk of Fractional Quantum Hall States

Authors: Xinlei Yue, Ady Stern

Abstract: We analyze electronic excitations (excitations generated by adding or removing one electron) in the bulk of fractional quantum Hall states in Jain sequence states, using composite fermion Chern-Simons field theory. Starting from meanfield approximation in which gauge field fluctuations are neglected, we use symmetry to constrain the possible composite fermion states contributing to electronic Gree… ▽ More We analyze electronic excitations (excitations generated by adding or removing one electron) in the bulk of fractional quantum Hall states in Jain sequence states, using composite fermion Chern-Simons field theory. Starting from meanfield approximation in which gauge field fluctuations are neglected, we use symmetry to constrain the possible composite fermion states contributing to electronic Green's function and expect discrete infinitely-sharp peaks in the electronic spectral function. We further consider the electronic excitations in particle-hole conjugate fractional quantum hall states. Gauge field fluctuations play an increasingly important role in the electron spectral function as the filling factor approaches 1/2, and evolve the discrete coherent peaks into a broad continuum even in the absence of impurities. At that limit, we switch to the electron perspective and calculate the electron spectral function via linked cluster approximation from the low to intermediate energy range. Finally, we compare our results with recent experiments. △ Less

Submitted 20 September, 2024; v1 submitted 13 June, 2024; originally announced June 2024.

Journal ref: Phys. Rev. B 110, 115428 (2024)

Ring states in topological materials

Authors: Raquel Queiroz, Roni Ilan, Zhida Song, B. Andrei Bernevig, Ady Stern

Abstract: Ingap states are commonly observed in semiconductors and are often well characterized by a hydrogenic model within the effective mass approximation. However, when impurities are strong, they significantly perturb all momentum eigenstates, leading to deep-level bound states that reveal the global properties of the unperturbed band structure. In this work, we discover that the topology of band wavef… ▽ More Ingap states are commonly observed in semiconductors and are often well characterized by a hydrogenic model within the effective mass approximation. However, when impurities are strong, they significantly perturb all momentum eigenstates, leading to deep-level bound states that reveal the global properties of the unperturbed band structure. In this work, we discover that the topology of band wavefunctions can impose zeros in the impurity-projected Green's function within topological gaps. These zeros can be interpreted as spectral attractors, defining the energy at which ingap states are pinned in the presence of infinitely strong local impurities. Their pinning energy is found by minimizing the level repulsion of band eigenstates onto the ingap state. We refer to these states as ring states, marked by a mixed band character and a node at the impurity site, guaranteeing their orthogonality to the bare impurity eigenstates and a weak energy dependence on the impurity strength. We show that the inability to construct symmetric and exponentially localized Wannier functions ensures topological protection of ring states. Linking ring states together, the edge or surface modes can be recovered for any topologically protected phase. Therefore, ring states can also be viewed as building blocks of boundary modes, offering a framework to understand bulk-boundary correspondence. △ Less

Submitted 5 June, 2024; originally announced June 2024.

Comments: 12 pages, 5 figures + 20 pages supplementary material

Even Integer Quantum Hall Effect in Materials with Hidden Spin Texture

Authors: Daniel Kaplan, Ady Stern, Binghai Yan

Abstract: Because spin-orbit coupling (SOC) is invisible in the band structure when inversion symmetry exists, whether spins are trivially degenerate or strongly coupled to momentum due to SOC is presumed to make little difference in transport measurements, such as magnetoresistance and quantum oscillations. In this work, however, we show that hidden Rashba SOC in a centrosymmetric two-dimensional material… ▽ More Because spin-orbit coupling (SOC) is invisible in the band structure when inversion symmetry exists, whether spins are trivially degenerate or strongly coupled to momentum due to SOC is presumed to make little difference in transport measurements, such as magnetoresistance and quantum oscillations. In this work, however, we show that hidden Rashba SOC in a centrosymmetric two-dimensional material can lead to the quantum Hall effect with only even-integer plateaus, unlike a spinless electron gas. Here, two Rashba layers that are degenerate but with opposite SOC due to inversion symmetry, hybridize with each other and create two doubly-degenerate bands with hidden spin texture. Correspondingly, two branches of Landau levels interact, resulting in significant suppression of spin splitting due to the balancing of intralayer SOC and interlayer hybridization. Furthermore, we show that breaking inversion symmetry restores the ordinary quantum Hall fluid by introducing spin-split Fermi surfaces. Our theory can apply to centrosymmetric materials with strong SOC, as demonstrated in a recent experiment on the two-dimensional semiconductor Bi$_2$O$_2$Se. △ Less

Submitted 5 June, 2024; originally announced June 2024.

Comments: 11 pages + appendices

Identifying the topological order of quantized half-filled Landau levels through their daughter states

Authors: Evgenii Zheltonozhskii, Ady Stern, Netanel H. Lindner

Abstract: Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary series of Abelian fractional quantum Hall states that emerge above and below the half-filling point. On a particular side of half-filling, each series may origi… ▽ More Fractional quantum Hall states at a half-filled Landau level are believed to carry an integer number $\mathcal{C}$ of chiral Majorana edge modes, reflected in their thermal Hall conductivity. We show that this number determines the primary series of Abelian fractional quantum Hall states that emerge above and below the half-filling point. On a particular side of half-filling, each series may originate from two consecutive values of $\mathcal{C}$, but the combination of the series above and below half-filling uniquely identifies $\mathcal{C}$. We analyze these states both by a hierarchy approach and by a composite fermion approach. In the latter, we map electrons near a half-filled Landau level to composite fermions at a weak magnetic field and show that a bosonic integer quantum Hall state is formed by pairs of composite fermions and plays a crucial role in the state's Hall conductivity. △ Less

Submitted 9 December, 2024; v1 submitted 6 May, 2024; originally announced May 2024.

Journal ref: Phys. Rev. B 110, 245140 - Published 26 December, 2024

Flat bands in chiral multilayer graphene

Authors: Roi Makov, Francisco Guinea, Ady Stern

Abstract: We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts, in a way that preserves a set of symmetries, we define a two-dimensional parameter plane that hosts lines of two and four flat bands. This plane enables adiabat… ▽ More We study the formation and properties of perfectly-flat zero energy bands in a multi-layer graphene systems in the chiral limit. Employing the degrees of freedoms of the multi-layer system, such as relative twist-angle and relative shifts, in a way that preserves a set of symmetries, we define a two-dimensional parameter plane that hosts lines of two and four flat bands. This plane enables adiabatic continuation of multi-layer chiral systems to weakly coupled bi- and tri-layer systems, and through that mapping provides tools for calculating the Chern numbers of the flat bands. We show that a flat band of Chern number $C$ can be spanned by $C$ effective Landau levels, all experiencing an effective flux of $1/C$ flux quantum per unit cell, and each carrying its own intra-unit-cell wave function. The flat bands do not disperse under the effect of a perpendicular magnetic field, and the gap to the dispersive bands closes when the externally applied flux cancels the $1/C$ effective flux. △ Less

Submitted 24 April, 2024; originally announced April 2024.

Comments: 16 pages, 11 figures

Even-integer Quantum Hall Effect in an Oxide Caused by Hidden Rashba Effect

Authors: Jingyue Wang, Junwei Huang, Daniel Kaplan, Xuehan Zhou, Congwei Tan, Jing Zhang, Gangjian Jin, Xuzhong Cong, Yongchao Zhu, Xiaoyin Gao, Yan Liang, Huakun Zuo, Zengwei Zhu, Ruixue Zhu, Ady Stern, Hongtao Liu, Peng Gao, Binghai Yan, Hongtao Yuan, Hailin Peng

Abstract: In the presence of high magnetic field, quantum Hall systems usually host both even- and odd-integer quantized states because of lifted band degeneracies. Selective control of these quantized states is challenging but essential to understand the exotic ground states and manipulate the spin textures. Here, we study the quantum Hall effect in Bi2O2Se thin films. In magnetic fields as high as 50 T, w… ▽ More In the presence of high magnetic field, quantum Hall systems usually host both even- and odd-integer quantized states because of lifted band degeneracies. Selective control of these quantized states is challenging but essential to understand the exotic ground states and manipulate the spin textures. Here, we study the quantum Hall effect in Bi2O2Se thin films. In magnetic fields as high as 50 T, we observe only even-integer quantum Hall states, but no sign of odd-integer states. However, when reducing the thickness of the epitaxial Bi2O2Se film to one unit cell, we observe both odd- and even-integer states in this Janus (asymmetric) film grown on SrTiO3. By means of a Rashba bilayer model based on ab initio band structures of Bi2O2Se thin films, we can ascribe the absence of odd-integer states in thicker films to the hidden Rasbha effect, where the local inversion symmetry breaking in two sectors of the [Bi2O2]2+ layer yields opposite Rashba spin polarizations, which compensate with each other. In the one unit cell Bi2O2Se film grown on SrTiO3, the asymmetry introduced by top surface and bottom interface induces a net polar field. The resulting global Rashba effect lifts the band degeneracies present in the symmetric case of thicker films. △ Less

Submitted 28 June, 2024; v1 submitted 31 March, 2024; originally announced April 2024.

Comments: 6 Figures, 23 pages

Journal ref: Nature Nanotechnology 19, 1452-1459 (2024)

Compressible quantum liquid with vanishing Drude weight

Authors: Ahmed Abouelkomsan, Nisarga Paul, Ady Stern, Liang Fu

Abstract: We explore the possibility of quantum liquids that are compressible but have vanishing DC conductivity in the absence of disorder. We show that the composite Fermi liquid emerging from strong interaction in a generic Chern band has zero Drude weight, in stark contrast to normal Fermi liquids. Our work establishes the absence of Drude weight as the defining property of the composite Fermi liquid ph… ▽ More We explore the possibility of quantum liquids that are compressible but have vanishing DC conductivity in the absence of disorder. We show that the composite Fermi liquid emerging from strong interaction in a generic Chern band has zero Drude weight, in stark contrast to normal Fermi liquids. Our work establishes the absence of Drude weight as the defining property of the composite Fermi liquid phase, which distinguishes it from the Fermi liquid or other types of non-Fermi liquids. Our findings point to a possibly wide class of gapless quantum phases with unexpected transport and optical properties. △ Less

Submitted 1 May, 2025; v1 submitted 21 March, 2024; originally announced March 2024.

Comments: 5 + 6, published version

Journal ref: Phys. Rev. Lett. 134, 176501 (2025)

Theory of Half-Integer Fractional Quantum Spin Hall Insulator Edges

Authors: Julian May-Mann, Ady Stern, Trithep Devakul

Abstract: We study the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states can be viewed as symmetric combinations of a spin-up and spin-down half-integer fractional quantum Hall state (FQH) that are time-reversal invariant, and conserve the z-component of spin. We consider the non-Abelian states based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, and… ▽ More We study the edges of fractional quantum spin Hall insulators (FQSH) with half-integer spin Hall conductance. These states can be viewed as symmetric combinations of a spin-up and spin-down half-integer fractional quantum Hall state (FQH) that are time-reversal invariant, and conserve the z-component of spin. We consider the non-Abelian states based on the Pfaffian, anti-Pfaffian, PH-Pfaffian, and 221 FQH, and generic Abelian FQH. For strong enough spin-conserving interactions, we find that all the non-Abelian and Abelian edges flow to the same fixed point that consists of a single pair of charged counter-propagating bosonic modes. If spin-conservation is broken, the Abelian edge can be fully gapped in a time-reversal symmetric fashion. The non-Abelian edge with broken spin-conservation remains gapless due to time-reversal symmetry, and can flow to a new fixed point with a helical gapless pair of Majorana fermions. We discuss the possible relevance of our results to the recent observation of a half-integer edge conductance in twisted MoTe2. △ Less

Submitted 4 March, 2024; originally announced March 2024.

Comments: 9 pages

Aharonov-Bohm interference and the evolution of phase jumps in fractional quantum Hall Fabry-Perot interferometers based on bi-layer graphene

Authors: Jehyun Kim, Himanshu Dev, Ravi Kumar, Alexey Ilin, André Haug, Vishal Bhardwaj, Changki Hong, Kenji Watanabe, Takashi Taniguchi, Ady Stern, Yuval Ronen

Abstract: Quasi-particles in fractional quantum Hall states are collective excitations that carry fractional charge and anyonic statistics. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, the anyonic statistics is most notable in quantum interference phenomena. In this study, we utilize a versatile bilayer graphene-based Fabry-Pérot Interferometer… ▽ More Quasi-particles in fractional quantum Hall states are collective excitations that carry fractional charge and anyonic statistics. While the fractional charge affects semi-classical characteristics such as shot noise and charging energies, the anyonic statistics is most notable in quantum interference phenomena. In this study, we utilize a versatile bilayer graphene-based Fabry-Pérot Interferometer (FPI) that facilitates the study of a broad spectrum of operating regimes, from Coulomb-dominated to Aharonov-Bohm, for both integer and fractional quantum Hall states. Focusing on the $ν$=$1 \over 3$ fractional quantum Hall state, we study the Aharonov-Bohm interference of quasi-particles when the magnetic flux through an interference loop and the charge density within the loop are independently varied. When their combined variation is such that the Landau filling remains $1 \over 3$ we observe pristine Aharonov-Bohm oscillations with a period of three flux quanta, as is expected from the interference of quasi-particles of one-third of the electron charge. When the combined variation is such that it leads to quasi-particles addition or removal from the loop, phase jumps emerge, and alter the phase evolution. Notably, across all cases, the average phase consistently increases by 2$π$ with each addition of one electron to the loop. △ Less

Submitted 19 February, 2024; originally announced February 2024.

Current Induced Hidden States in Josephson Junctions

Authors: Shaowen Chen, Seunghyun Park, Uri Vool, Nikola Maksimovic, David A. Broadway, Mykhailo Flaks, Tony X. Zhou, Patrick Maletinsky, Ady Stern, Bertrand I. Halperin, Amir Yacoby

Abstract: Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field r… ▽ More Josephson junctions enable dissipation-less electrical current through metals and insulators below a critical current. Despite being central to quantum technology based on superconducting quantum bits and fundamental research into self-conjugate quasiparticles, the spatial distribution of super current flow at the junction and its predicted evolution with current bias and external magnetic field remain experimentally elusive. Revealing the hidden current flow, featureless in electrical resistance, helps understanding unconventional phenomena such as the nonreciprocal critical current, i.e., Josephson diode effect. Here we introduce a platform to visualize super current flow at the nanoscale. Utilizing a scanning magnetometer based on nitrogen vacancy centers in diamond, we uncover competing ground states electrically switchable within the zero-resistance regime. The competition results from the superconducting phase re-configuration induced by the Josephson current and kinetic inductance of thin-film superconductors. We further identify a new mechanism for the Josephson diode effect involving the Josephson current induced phase. The nanoscale super current flow emerges as a new experimental observable for elucidating unconventional superconductivity, and optimizing quantum computation and energy-efficient devices. △ Less

Submitted 13 August, 2024; v1 submitted 4 February, 2024; originally announced February 2024.

Transport properties of a half-filled Chern band at the electron and composite fermion phases

Authors: Ady Stern, Liang Fu

Abstract: We consider a half-filled Chern band and its transport properties in two phases that it may form, the electronic Fermi liquid and the composite-fermion Fermi liquid. For weak disorder, we show that the Hall resistivity for the former phase is very small, while for the latter it is close to $2h/e^2$, independent of the distribution of the Berry curvature in the band. At rising temperature and high… ▽ More We consider a half-filled Chern band and its transport properties in two phases that it may form, the electronic Fermi liquid and the composite-fermion Fermi liquid. For weak disorder, we show that the Hall resistivity for the former phase is very small, while for the latter it is close to $2h/e^2$, independent of the distribution of the Berry curvature in the band. At rising temperature and high frequency, we expect the Hall resistivity of the electronic phase to rise, and that of the composite-fermion phase to deviate from $2h/e^2$. At high frequency, sign changes are expected as well. Considering high-frequency transport, we show that the composite fermion phase carries a gapped plasmon mode which does not originate from long ranged Coulomb interaction, and we show how this mode, together with the reflection of electro-magnetic waves off the Chern band, allow for a measurement of the composite-fermion Drude weight and Berry curvature. Finally, we consider a scenario of a mixed-phase transition between the two phases, for example as a function of displacement-field, and show that such transition involves an enhancement of the longitudinal resistivity, as observed experimentally. △ Less

Submitted 28 November, 2023; originally announced November 2023.

Comments: 6 pages

Josephson junction arrays as a platform for topological phases of matter

Authors: Omri Lesser, Ady Stern, Yuval Oreg

Abstract: Two-dimensional arrays of superconductors separated by normal metallic regions exhibit rich phenomenology and a high degree of controllability. We establish such systems as platforms for topological phases of matter, and in particular chiral topological superconductivity. We propose and theoretically analyze several minimal models for this chiral phase based on commonly available superconductor-se… ▽ More Two-dimensional arrays of superconductors separated by normal metallic regions exhibit rich phenomenology and a high degree of controllability. We establish such systems as platforms for topological phases of matter, and in particular chiral topological superconductivity. We propose and theoretically analyze several minimal models for this chiral phase based on commonly available superconductor-semiconductor heterostructures. The topological transitions can be adjusted using a time-reversal-symmetry breaking knob, which can be activated by controlling the phases in the islands, introducing flux through the system, or applying an in-plane exchange field. We demonstrate transport signatures of the chiral topological phase that are unlikely to be mimicked by local non-topological effects. The flexibility and tunability of our platforms, along with the clear-cut experimental fingerprints, make for a viable playground for exploring chiral superconductivity in two dimensions. △ Less

Submitted 28 August, 2023; originally announced August 2023.

Comments: 11 pages, 8 figures

Heat Conductance of the Quantum Hall Bulk

Authors: Ron Aharon Melcer, Avigail Gil, Arup-Kumar Paul, Priya Tiwary, Vladimir Umansky, Moty Heiblum, Yuval Oreg, Ady Stern, Erez Berg

Abstract: The Quantum Hall Effect (QHE) is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions, and disorder. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density. Still, the details of the localized states and their contributi… ▽ More The Quantum Hall Effect (QHE) is a prototypical realization of a topological state of matter. It emerges from a subtle interplay between topology, interactions, and disorder. The disorder enables the formation of localized states in the bulk that stabilize the quantum Hall states with respect to the magnetic field and carrier density. Still, the details of the localized states and their contribution to transport remain beyond the reach of most experimental techniques. Here, we describe an extensive study of the bulk's heat conductance. Using a novel 'multi-terminal' short device (on a scale of $10 μm$), we separate the longitudinal thermal conductance, $κ_{xx}T$ (due to bulk's contribution), from the topological transverse value $κ_{xy}T$, by eliminating the contribution of the edge modes. When the magnetic field is tuned away from the conductance plateau center, the localized states in the bulk conduct heat efficiently ($κ_{xx}T \propto T$), while the bulk remains electrically insulating. Fractional states in the first excited Landau level, such as the $ν=7/3$ and $ν=5/2$, conduct heat throughout the plateau with a finite $κ_{xx} T$. We propose a theoretical model that identifies the localized states as the cause of the finite heat conductance, agreeing qualitatively with our experimental findings. △ Less

Submitted 15 September, 2023; v1 submitted 26 June, 2023; originally announced June 2023.

Comments: 30 pages 11 figures

Nonlinear response of 2DEG in the quantum Hall regime

Authors: Shuichi Iwakiri, Lev V. Ginzburg, Marc P. Röösli, Yigal Meir, Ady Stern, Christian Reichl, Matthias Berl, Werner Wegscheider, Thomas Ihn, Klaus Ensslin

Abstract: Breaking of inversion symmetry leads to nonlinear and nonreciprocal electron transport, in which the voltage response does not invert with the reversal of the current direction. Many systems have incorporated inversion symmetry breaking into their band or crystal structures. In this work, we demonstrate that a conventional two-dimensional electron gas (2DEG) system with a back gate shows non-recip… ▽ More Breaking of inversion symmetry leads to nonlinear and nonreciprocal electron transport, in which the voltage response does not invert with the reversal of the current direction. Many systems have incorporated inversion symmetry breaking into their band or crystal structures. In this work, we demonstrate that a conventional two-dimensional electron gas (2DEG) system with a back gate shows non-reciprocal behavior (with voltage proportional to current squared) in the quantum Hall regime, which depends on the out-of-plane magnetic field and contact configuration. The inversion symmetry is broken due to the presence of the back gate and magnetic field, and our phenomenological model provides a qualitative explanation of the experimental data. Our results suggest a universal mechanism that gives rise to non-reciprocal behavior in gated samples. △ Less

Submitted 16 June, 2023; originally announced June 2023.

Comments: 8 pages, 6 figures

Journal ref: Phys. Rev. Research 5, L032046 (2023)

Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry

Authors: Fa-Jie Wang, Zhen-Yu Xiao, Raquel Queiroz, B. Andrei Bernevig, Ady Stern, Zhi-Da Song

Abstract: Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magn… ▽ More Transitions between distinct obstructed atomic insulators (OAIs) protected by crystalline symmetries, where electrons form molecular orbitals centering away from the atom positions, must go through an intermediate metallic phase. In this work, we find that the intermediate metals will become a scale-invariant critical metal phase (CMP) under certain types of quenched disorder that respect the magnetic crystalline symmetries on average. We explicitly construct models respecting average $C_{2z}T$, $m$, and $C_{4z}T$ and show their scale-invariance under chemical potential disorder by the finite-size scaling method. Conventional theories, such as weak anti-localization and topological phase transition, cannot explain the underlying mechanism. A quantitative mapping between lattice and network models shows that the CMP can be understood through a semi-classical percolation problem. Ultimately, we systematically classify all the OAI transitions protected by (magnetic) groups $Pm$, $P2'$, $P4'$, and $P6'$ with and without spin-orbit coupling, most of which can support CMP. △ Less

Submitted 21 February, 2024; v1 submitted 7 June, 2023; originally announced June 2023.

Journal ref: Nat. Commun. 15(1), 3069 (2024)

Spatial adiabatic passage of ultracold atoms in optical tweezers

Authors: Yanay Florshaim, Elad Zohar, David Zeev Koplovich, Ilan Meltzer, Rafi Weill, Jonathan Nemirovsky, Amir Stern, Yoav Sagi

Abstract: Spatial adiabatic passage (SAP) is a process that facilitates the transfer of a wave packet between two localized modes that are not directly coupled, but rather interact through an intermediate third mode. By employing a counter-intuitive adiabatic pulse sequence, this technique achieves minimal population in the intermediate state and high transfer efficiency. Here, we report the implementation… ▽ More Spatial adiabatic passage (SAP) is a process that facilitates the transfer of a wave packet between two localized modes that are not directly coupled, but rather interact through an intermediate third mode. By employing a counter-intuitive adiabatic pulse sequence, this technique achieves minimal population in the intermediate state and high transfer efficiency. Here, we report the implementation of SAP for transferring massive particles between three micro-optical traps. We begin by preparing ultracold fermionic atoms in low vibrational eigenstates of one trap and then manipulate the distance between the three traps to execute the SAP protocol. We observe a smooth transfer of atoms between the two outer traps, accompanied by a low population in the central trap. We validate our findings and underscore the significance of the counter-intuitive sequence by reversing the order of the pulse sequence. Additionally, we investigate the influence of the tunneling rate and the time delay between the motion of the two external tweezers on the fidelity of the process. Our results open up new possibilities for advanced control and manipulation schemes in optical tweezer array platforms. △ Less

Submitted 25 May, 2023; originally announced May 2023.

Comments: 6 pages, 4 figures

Journal ref: Sci. Adv. 10, eadl1220 (2024)

Stoner ferromagnetism in a momentum-confined interacting 2D electron gas

Authors: Ohad Antebi, Ady Stern, Erez Berg

Abstract: In this work we investigate the ground state of a momentum-confined interacting 2D electron gas, a momentum-space analog of an infinite quantum well. The study is performed by combining analytical results with a numerical exact diagonalization procedure. We find a ferromagnetic ground state near a particular electron density and for a range of effective electron (or hole) masses. We argue that thi… ▽ More In this work we investigate the ground state of a momentum-confined interacting 2D electron gas, a momentum-space analog of an infinite quantum well. The study is performed by combining analytical results with a numerical exact diagonalization procedure. We find a ferromagnetic ground state near a particular electron density and for a range of effective electron (or hole) masses. We argue that this observation may be relevant to the generalized Stoner ferromagnetism recently observed in multilayer graphene systems. The collective magnon excitations exhibit a linear dispersion, which originates from a diverging spin stiffness. △ Less

Submitted 18 April, 2024; v1 submitted 22 May, 2023; originally announced May 2023.

Comments: 4 pages, 4 figures + supplemental material

Aharonov-Bohm magnetism in open Fermi surfaces

Authors: Kostas Vilkelis, Ady Stern, Anton Akhmerov

Abstract: Orbital diamagnetism requires closed orbits according to the Liftshiftz-Kosevich theory. Therefore, one might expect that open Fermi surfaces do not have a diamagnetic response. Contrary to this expectation, we show that open orbits in finite systems do contribute a magnetic response which oscillates between diamagnetism and paramagnetism. The oscillations are similar to the Aharonov-Bohm effect,… ▽ More Orbital diamagnetism requires closed orbits according to the Liftshiftz-Kosevich theory. Therefore, one might expect that open Fermi surfaces do not have a diamagnetic response. Contrary to this expectation, we show that open orbits in finite systems do contribute a magnetic response which oscillates between diamagnetism and paramagnetism. The oscillations are similar to the Aharonov-Bohm effect, because the oscillation phase is set by the number of flux quanta through the area defined by the width of the sample and the distance between adjacent atomic layers. The magnetic response originates from the closed trajectories formed by counter-propagating open orbits coupled via specular boundary reflections. The phenomenon acts as a probe of the phase coherence of open electron trajectories. △ Less

Submitted 7 March, 2023; originally announced March 2023.

Transport Signatures of Fractional Quantum Hall Binding Transitions

Authors: Christian Spånslätt, Ady Stern, Alexander D. Mirlin

Abstract: Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a ``binding transition'' remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling $ν=9/5$. We demonstrate theoreticall… ▽ More Certain fractional quantum Hall edges have been predicted to undergo quantum phase transitions which reduce the number of edge channels and at the same time bind electrons together. However, detailed studies of experimental signatures of such a ``binding transition'' remain lacking. Here, we propose quantum transport signatures with focus on the edge at filling $ν=9/5$. We demonstrate theoretically that in the regime of non-equilibrated edge transport, the bound and unbound edge phases have distinct conductance and noise characteristics. We also show that for a quantum point contact in the strong back-scattering regime, the bound phase produces a minimum Fano-factor $F_{SBS}=3$ corresponding to three-electron tunneling, whereas single electron tunneling is strongly suppressed at low energies. Together with recent experimental developments, our results will be useful for detecting binding transitions in the fractional quantum Hall regime. △ Less

Submitted 11 February, 2023; originally announced February 2023.

Comments: 17 pages, 6 figures

Journal ref: Phys. Rev. B 107, 245405 (2023)

Anyon statistics through conductance measurements of time-domain interferometry

Authors: Noam Schiller, Yotam Shapira, Ady Stern, Yuval Oreg

Abstract: We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly d… ▽ More We propose a method to extract the mutual exchange statistics of the anyonic excitations of a general Abelian fractional quantum Hall state, by comparing the tunneling characteristics of a quantum point contact in two different experimental conditions. In the first, the tunneling current between two edges at different chemical potentials is measured. In the second, one of these edges is strongly diluted by an earlier point contact. We describe the case of the dilute beam in terms of a time-domain interferometer between the anyons flowing along the edge and quasiparticle-quasihole excitations created at the tunneling quantum point contact. In both cases, temperature is kept large, such that the measured current is given to linear response. Remarkably, our proposal does not require the measurement of current correlations, and allows us to carefully separate effects of the fractional charge and statistics from effects of intra- and inter-edge interactions. △ Less

Submitted 30 December, 2022; originally announced January 2023.

Comments: 5+5 pages, 2 figures

The Quantum Twisting Microscope

Authors: Alon Inbar, John Birkbeck, Jiewen Xiao, Takashi Taniguchi, Kenji Watanabe, Binghai Yan, Yuval Oreg, Ady Stern, Erez Berg, Shahal Ilani

Abstract: The invention of scanning probe microscopy has revolutionized the way electronic phenomena are visualized. While present-day probes can access a variety of electronic properties at a single location in space, a scanning microscope that can directly probe the quantum mechanical existence of an electron at multiple locations would provide direct access to key quantum properties of electronic systems… ▽ More The invention of scanning probe microscopy has revolutionized the way electronic phenomena are visualized. While present-day probes can access a variety of electronic properties at a single location in space, a scanning microscope that can directly probe the quantum mechanical existence of an electron at multiple locations would provide direct access to key quantum properties of electronic systems, so far unreachable. Here, we demonstrate a conceptually new type of scanning probe microscope - the Quantum Twisting Microscope (QTM) - capable of performing local interference experiments at its tip. The QTM is based on a unique van-der-Waals tip, allowing the creation of pristine 2D junctions, which provide a multitude of coherently-interfering paths for an electron to tunnel into a sample. With the addition of a continuously scanned twist angle between the tip and sample, this microscope probes electrons in momentum space similar to the way a scanning tunneling microscope probes electrons in real space. Through a series of experiments, we demonstrate room temperature quantum coherence at the tip, study the twist angle evolution of twisted bilayer graphene, directly image the energy bands of monolayer and twisted bilayer graphene, and finally, apply large local pressures while visualizing the evolution of the flat energy bands of the latter. The QTM opens the way for novel classes of experiments on quantum materials. △ Less

Submitted 10 August, 2022; originally announced August 2022.

Degenerate Raman sideband cooling of 40K atoms

Authors: Elad Zohar, Yanay Florshaim, Oded Zilberman, Amir Stern, Yoav Sagi

Abstract: We report on the implementation of degenerate Raman sideband cooling of $^{40}$K atoms. The scheme incorporates a 3D optical lattice, which confines the atoms and drives the Raman transitions. The optical cooling cycle is closed by two optical pumping beams. The wavelength of the laser beams forming the lattice is close to the D$_2$ atomic transition, while the optical pumping is operated near the… ▽ More We report on the implementation of degenerate Raman sideband cooling of $^{40}$K atoms. The scheme incorporates a 3D optical lattice, which confines the atoms and drives the Raman transitions. The optical cooling cycle is closed by two optical pumping beams. The wavelength of the laser beams forming the lattice is close to the D$_2$ atomic transition, while the optical pumping is operated near the D$_1$ transition. With this cooling method, we achieve temperature of $\sim$$1μ$K of a cloud with $\sim$$10^7$ atoms. This corresponds to a phase space density of $\ge$$10^{-3}$. Moreover, the fermionic ensemble is spin polarized to conditions which are favorable for subsequent evaporative cooling. We study the dependence of the cooling scheme on several parameters, including the applied magnetic field, the detuning, duration, and intensity profile of the optical pumping beams. Adding this optical cooling stage to current Fermi gas experiments can improve the final conditions and increase the data rate. △ Less

Submitted 10 August, 2022; originally announced August 2022.

Comments: 7 pages, 7 figures

One-dimensional topological superconductivity based entirely on phase control

Authors: Omri Lesser, Yuval Oreg, Ady Stern

Abstract: Topological superconductivity in one dimension requires time-reversal symmetry breaking, but at the same time it is hindered by external magnetic fields. We offer a general prescription for inducing topological superconductivity in planar superconductor-normal-superconductor-normal-superconductor (SNSNS) Josephson junctions without applying any magnetic fields on the junctions. Our platform relies… ▽ More Topological superconductivity in one dimension requires time-reversal symmetry breaking, but at the same time it is hindered by external magnetic fields. We offer a general prescription for inducing topological superconductivity in planar superconductor-normal-superconductor-normal-superconductor (SNSNS) Josephson junctions without applying any magnetic fields on the junctions. Our platform relies on two key ingredients: the three parallel superconductors form two SNS junctions with phase winding, and the Fermi velocities for the two spin branches transverse to the junction must be different from one another. The two phase differences between the three superconductors define a parameter plane which includes large topological regions. We analytically derive the critical curves where the topological phase transitions occur, and corroborate the result with a numerical calculation based on a tight-binding model. We further propose material platforms with unequal Fermi velocities, establishing the experimental feasibility of our approach. △ Less

Submitted 27 June, 2022; originally announced June 2022.

Comments: 5+10 pages, 3+8 figures

Journal ref: Phys. Rev. B 106, L241405 (2022)

Local and Nonlocal Transport Spectroscopy in Planar Josephson Junctions

Authors: A. Banerjee, O. Lesser, M. A. Rahman, C. Thomas, T. Wang, M. J. Manfra, E. Berg, Y. Oreg, Ady Stern, C. M. Marcus

Abstract: We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs/Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2 x 2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the jun… ▽ More We report simultaneously acquired local and nonlocal transport spectroscopy in a phase-biased planar Josephson junction based on an epitaxial InAs/Al hybrid two-dimensional heterostructure. Quantum point contacts at the junction ends allow measurement of the 2 x 2 matrix of local and nonlocal tunneling conductances as a function of magnetic field along the junction, phase difference across the junction, and carrier density. A closing and reopening of a gap was observed in both the local and nonlocal tunneling spectra as a function of magnetic field. For particular tunings of junction density, gap reopenings were accompanied by zero-bias conductance peaks (ZBCPs) in local conductances. End-to-end correlation of gap reopening was strong, while correlation of local ZBCPs was weak. A simple, disorder-free model of the device shows comparable conductance matrix behavior associated with a topological phase transition. Phase dependence helps distinguish possible origins of the ZBCPs. △ Less

Submitted 19 May, 2022; originally announced May 2022.

Report number: NBI QDEV 2022

Journal ref: Phys. Rev. Lett. 130, 096202 (2023)

Symmetries as the guiding principle for flattening bands of Dirac fermions

Authors: Yarden Sheffer, Raquel Queiroz, Ady Stern

Abstract: Since the discovery of magic-angle twisted bilayer graphene (TBG), flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, g… ▽ More Since the discovery of magic-angle twisted bilayer graphene (TBG), flat bands in Dirac materials have become a prominent platform for realizing strong correlation effects in electronic systems. Here we show that the symmetry group protecting the Dirac cone in such materials determines whether a Dirac band may be flattened by the tuning of a small number of parameters. We devise a criterion that, given a symmetry group, allows for the calculation of the number of parameters required to make the Dirac velocity vanish. This criterion is employed to study band flattening in twisted bilayer graphene and in surface states of 3D topological insulators. Following this discussion, we identify the symmetries under which the vanishing of the Dirac velocity implies the emergence of perfectly-flat bands. Our analysis allows us to construct additional model Hamiltonians that display perfectly-flat bands at certain points in the space of parameters: the first is a toy model of two coupled 3D TI surfaces, and the second is a quasi-crystalline generalization of the chiral model of TBG. △ Less

Submitted 29 March, 2023; v1 submitted 5 May, 2022; originally announced May 2022.

Comments: 21 pages, 12 figures, Accepted to Physical Review x

Superconductivity and fermionic dissipation in quantum Hall edges

Authors: Noam Schiller, Barak A. Katzir, Ady Stern, Erez Berg, Netanel H. Lindner, Yuval Oreg

Abstract: Proximity-induced superconductivity in fractional quantum Hall edges is a prerequisite to proposed realizations of parafermion zero-modes. A recent experimental work [Gül et al., Phys. Rev. X 12, 021057 (2022)] provided evidence for such coupling, in the form of a crossed Andreev reflection signal, in which electrons enter a superconductor from one chiral mode and are reflected as holes to another… ▽ More Proximity-induced superconductivity in fractional quantum Hall edges is a prerequisite to proposed realizations of parafermion zero-modes. A recent experimental work [Gül et al., Phys. Rev. X 12, 021057 (2022)] provided evidence for such coupling, in the form of a crossed Andreev reflection signal, in which electrons enter a superconductor from one chiral mode and are reflected as holes to another, counter-propagating chiral mode. Remarkably, while the probability for crossed Andreev reflection was small, it was stronger for $ν=1/3$ fractional quantum Hall edges than for integer ones. We theoretically explain these findings, including the relative strengths of the signals in the two cases and their qualitatively different temperature dependencies. An essential part of our model is the coupling of the edge modes to normal states in the cores of Abrikosov vortices induced by the magnetic field, which provide a fermionic bath. We find that the stronger crossed Andreev reflection in the fractional case originates from the suppression of electronic tunneling between the fermionic bath and the fractional quantum Hall edges. Our theory shows that the mere observation of crossed Andreev reflection signal does not necessarily imply the presence of localized parafermion zero-modes, and suggests ways to identify their presence from the behavior of this signal in the low temperature regime. △ Less

Submitted 17 April, 2023; v1 submitted 21 February, 2022; originally announced February 2022.

Comments: 5+11 pages, 4+1 figures. Short (12:22) video explanation of model and main results at https://www.youtube.com/watch?v=h0rS7TyUUMI

Imaging Chern mosaic and Berry-curvature magnetism in magic-angle graphene

Authors: Sameer Grover, Matan Bocarsly, Aviram Uri, Petr Stepanov, Giorgio Di Battista, Indranil Roy, Jiewen Xiao, Alexander Y. Meltzer, Yuri Myasoedov, Keshav Pareek, Kenji Watanabe, Takashi Taniguchi, Binghai Yan, Ady Stern, Erez Berg, Dmitri K. Efetov, Eli Zeldov

Abstract: Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curv… ▽ More Charge carriers in magic angle graphene come in eight flavors described by a combination of their spin, valley, and sublattice polarizations. When the inversion and time reversal symmetries are broken by the substrate or by strong interactions, the degeneracy of the flavors can be lifted and their corresponding bands can be filled sequentially. Due to their non-trivial band topology and Berry curvature, each of the bands is classified by a topological Chern number, leading to the quantum anomalous Hall and Chern insulator states at integer fillings $ν$ of the bands. It has been recently predicted, however, that depending on the local atomic-scale arrangements of the graphene and the encapsulating hBN lattices, rather than being a global topological invariant, the Chern number C may become position dependent, altering transport and magnetic properties of the itinerant electrons. Using a SQUID-on-tip, we directly image the nanoscale Berry-curvature-induced equilibrium orbital magnetism, the polarity of which is governed by the local Chern number, and detect its two constituent components associated with the drift and the self-rotation of the electronic wave packets. At $ν=1$, we observe local zero-field valley-polarized Chern insulators forming a mosaic of microscopic patches of C=-1, 0, or 1, governed by the local sublattice polarization, consistent with predictions. Upon further filling, we find a first-order phase transition due to recondensation of electrons from valley K to K', which leads to irreversible flips of the local Chern number and the magnetization, and to the formation of valley domain walls giving rise to hysteretic global anomalous Hall resistance. The findings shed new light on the structure and dynamics of topological phases and call for exploration of the controllable formation of flavor domain walls and their utilization in twistronic devices. △ Less

Submitted 28 April, 2022; v1 submitted 18 January, 2022; originally announced January 2022.

Comments: 29 pages, 5 main text figures and 8 supplementary figures

Journal ref: Nat. Phys. 18, 885-892 (2022)

Signatures of a topological phase transition in a planar Josephson junction

Authors: A. Banerjee, O. Lesser, M. A. Rahman, H. -R. Wang, M. -R. Li, A. Kringhøj, A. M. Whiticar, A. C. C. Drachmann, C. Thomas, T. Wang, M. J. Manfra, E. Berg, Y. Oreg, Ady Stern, C. M. Marcus

Abstract: A growing body of work suggests that planar Josephson junctions fabricated using superconducting hybrid materials provide a highly controllable route toward one-dimensional topological superconductivity. Among the experimental controls are in-plane magnetic field, phase difference across the junction, and carrier density set by electrostatic gate voltages. Here, we investigate planar Josephson jun… ▽ More A growing body of work suggests that planar Josephson junctions fabricated using superconducting hybrid materials provide a highly controllable route toward one-dimensional topological superconductivity. Among the experimental controls are in-plane magnetic field, phase difference across the junction, and carrier density set by electrostatic gate voltages. Here, we investigate planar Josephson junctions with an improved design based on an epitaxial InAs/Al heterostructure, embedded in a superconducting loop, probed with integrated quantum point contacts (QPCs) at both ends of the junction. For particular ranges of in-plane field and gate voltages, a closing and reopening of the superconducting gap is observed, along with a zero-bias conductance peak (ZBCP) that appears upon reopening of the gap. Consistency with a simple theoretical model supports the interpretation of a topological phase transition. While gap closings and reopenings generally occurred together at the two ends of the junction, the height, shape, and even presence of ZBCPs typically differed between the ends, presumably due to disorder and variation of couplings to local probes. △ Less

Submitted 10 January, 2022; originally announced January 2022.

Report number: NBI QDev 2022

In-plane orbital magnetization as a probe for symmetry breaking in strained twisted bilayer graphene

Authors: Ohad Antebi, Ady Stern, Erez Berg

Abstract: Three symmetries prevent a twisted bilayer of graphene from developing an in-plane spontaneous magnetization in the absence of a magnetic field - time reversal symmetry, $C_2$ symmetry to $π$ rotation and $C_3$ symmetry to $2π/3$ rotation. In contrast, there are experimental and theoretical indications that, at certain electron densities, time reversal and $C_2$ symmetries are broken spontaneously… ▽ More Three symmetries prevent a twisted bilayer of graphene from developing an in-plane spontaneous magnetization in the absence of a magnetic field - time reversal symmetry, $C_2$ symmetry to $π$ rotation and $C_3$ symmetry to $2π/3$ rotation. In contrast, there are experimental and theoretical indications that, at certain electron densities, time reversal and $C_2$ symmetries are broken spontaneously, while the $C_3$ symmetry is often broken due to strain. We show that in-plane orbital magnetization is a very sensitive probe to the simultaneous breaking of these three symmetries, exhibiting surprisingly large values (of the order of one Bohr magneton per moiré unit cell) for valley polarized states at rather small values of heterostrain. We attribute these large values to the large magnitude of the characteristic magnetization of individual Bloch states, which we find to reflect the fast Dirac velocity of single layer graphene, rather than the slow velocity of the twisted bilayer. These large values are forced to mutually cancel in valley-symmetric states, but the cancellation does not occur in valley-polarized states. Our analysis is carried out both for non-interacting electrons and within a simplified Hartree-Fock framework. △ Less

Submitted 29 December, 2021; originally announced December 2021.

Comments: 17 pages, 9 figures

Imaging Hydrodynamic Electrons Flowing Without Landauer-Sharvin Resistance

Authors: Chandan Kumar, John Birkbeck, Joseph A. Sulpizio, David J. Perello, Takashi Taniguchi, Kenji Watanabe, Oren Reuven, Thomas Scaffidi, Ady Stern, Andre K. Geim, Shahal Ilani

Abstract: Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen… ▽ More Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landuer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length scale predicted by hydrodynamic theories - the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies △ Less

Submitted 11 November, 2021; originally announced November 2021.

Spread and erase -- How electron hydrodynamics can eliminate the Landauer-Sharvin resistance

Authors: Ady Stern, Thomas Scaffidi, Oren Reuven, Chandan Kumar, John Birkbeck, Shahal Ilani

Abstract: It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bou… ▽ More It has long been realized that even a perfectly clean electronic system harbors a Landauer-Sharvin resistance, inversely proportional to the number of its conduction channels. This resistance is usually associated with voltage drops on the system's contacts to an external circuit. Recent theories have shown that hydrodynamic effects can reduce this resistance, raising the question of the lower bound of resistance of hydrodynamic electrons. Here we show that by a proper choice of device geometry, it is possible to spread the Landauer-Sharvin resistance throughout the bulk of the system, allowing its complete elimination by electron hydrodynamics. We trace the effect to the dynamics of electrons flowing in channels that terminate within the sample. For ballistic systems this termination leads to back-reflection of the electrons and creates resistance. Hydrodynamically, the scattering of these electrons off other electrons allows them to transfer to transmitted channels and avoid the resistance. Counter-intuitively, we find that in contrast to the ohmic regime, for hydrodynamic electrons the resistance of a device with a given width can decrease with its length, suggesting that a long enough device may have an arbitrarily small total resistance. △ Less

Submitted 20 November, 2022; v1 submitted 28 October, 2021; originally announced October 2021.

Comments: 6 pages, 3 figures for main text + 4 pages of supplemental material; revised version as published in PRL

Theory of correlated insulators and superconductivity in twisted bilayer graphene

Authors: Gal Shavit, Erez Berg, Ady Stern, Yuval Oreg

Abstract: We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional w… ▽ More We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at non-integer fillings. Adding a phonon-mediated inter-valley retarded attractive interaction, we obtain strong-coupling superconducting domes, whose structure is in qualitative agreement with experiments. Our model elucidates how the intricate form of the interactions and the particle-hole asymmetry of the electronic structure determine the phase diagram. It also explains how subtle differences between devices may lead to the different behaviors observed experimentally. A similar model can be applied with minor modifications to other moiré systems, such as twisted trilayer graphene. △ Less

Submitted 13 December, 2021; v1 submitted 18 July, 2021; originally announced July 2021.

Comments: Published version

Journal ref: Phys. Rev. Lett. 127, 247703 (2021)

Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators

Authors: Yarden Sheffer, Ady Stern

Abstract: We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external fie… ▽ More We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field. △ Less

Submitted 11 September, 2021; v1 submitted 20 June, 2021; originally announced June 2021.

Comments: 10 pages, 2 figures

Journal ref: Phys. Rev. B 104, 121405 (2021)

Identifying the $ν=\frac{5}{2}$ topological order through charge transport measurements

Authors: Misha Yutushui, Ady Stern, David F. Mross

Abstract: We propose an experiment to identify the topological order of the $ν=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $ν=2, \ \frac{5}{2}$ and $3$ in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measur… ▽ More We propose an experiment to identify the topological order of the $ν=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $ν=2, \ \frac{5}{2}$ and $3$ in the same device. Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements. Additionally, it distinguishes between the Moore-Read and Anti-Pfaffian topological orders, which are favored by numerical calculations. △ Less

Submitted 6 January, 2022; v1 submitted 14 June, 2021; originally announced June 2021.

Comments: 4 pages, 3 figures, 1 table, RPL version

Journal ref: Phys. Rev. Lett. 128, 016401 (2022)

Gapping fragile topological bands by interactions

Authors: Ari M. Turner, Erez Berg, Ady Stern

Abstract: We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaki… ▽ More We consider the stability of fragile topological bands protected by space-time inversion symmetry in the presence of strong electron-electron interactions. At the single-particle level, the topological nature of the bands prevents the opening of a gap between them. In contrast, we show that when the fragile bands are half filled, interactions can open a gap in the many-body spectrum without breaking any symmetry or mixing degrees of freedom from remote bands. Furthermore, the resulting ground state is not topologically ordered. Thus, a fragile topological band structure does not present an obstruction to forming a "featureless insulator" ground state. Our construction relies on the formation of fermionic bound states of two electrons and one hole, known as "trions". The trions form a band whose coupling to the electronic band enables the gap opening. This result may be relevant to the gapped state indicated by recent experiments in magic angle twisted bilayer graphene at charge neutrality. △ Less

Submitted 18 February, 2022; v1 submitted 19 April, 2021; originally announced April 2021.

Comments: 10 pages, 6 figures. Added References, expanded Supplementary Information. See accompanying animation at https://youtu.be/78USiNqM8I0. Published version

Journal ref: Phys. Rev. Lett. 128, 056801 (2022)

Engineered platforms for topological superconductivity and Majorana zero modes

Authors: Karsten Flensberg, Felix von Oppen, Ady Stern

Abstract: Among the major approaches that are being pursued for realizing quantum bits, the Majorana-based platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologically-protected manner. The quantum information is protected by its nonlocal storage in localized and well-separated Majorana zero modes, and manipulated by exploiting their nona… ▽ More Among the major approaches that are being pursued for realizing quantum bits, the Majorana-based platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologically-protected manner. The quantum information is protected by its nonlocal storage in localized and well-separated Majorana zero modes, and manipulated by exploiting their nonabelian quantum exchange properties. Realizing these topological qubits is experimentally challenging, requiring superconductivity, helical electrons (created by spin-orbit coupling) and breaking of time reversal symmetry to all cooperate in an uncomfortable alliance. Over the past decade, several candidate material systems for realizing Majorana-based topological qubits have been explored, and there is accumulating, though still debated, evidence that zero modes are indeed being realized. This paper reviews the basic physical principles on which these approaches are based, the material systems that are being developed, and the current state of the field. We highlight both the progress made and the challenges that still need to be overcome. △ Less

Submitted 9 March, 2021; originally announced March 2021.

Comments: Review paper, to appear in Nature Reviews Materials

Report number: QDEV NBI CMT 2021

Novel method distinguishing between competing topological orders

Authors: Bivas Dutta, Wenmin Yang, Ron Aharon Melcer, Hemanta Kumar Kundu, Moty Heiblum, Vladimir Umansky, Yuval Oreg, Ady Stern, David Mross

Abstract: Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carrying electrons, fractional - carrying fractional charges; and neutral - carrying excitations with zero net charge but a well-defined amount of heat. The… ▽ More Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carrying electrons, fractional - carrying fractional charges; and neutral - carrying excitations with zero net charge but a well-defined amount of heat. The latter two may obey anyonic statistics, which can be abelian or non-abelian. The most-studied putative non-abelian state is the spin-polarized filling factor ν=5/2, whose charge e/4 quasiparticles are accompanied by neutral modes. This filling, however, permits different possible topological orders, which can be abelian or non-abelian. While numerical calculations favor the non-abelian anti-Pfaffian (A-Pf) order to have the lowest energy, recent thermal conductance measurements suggested the experimentally realized order to be the particle-hole Pfaffian (PH-Pf) order. It has been suggested that lack of thermal equilibration among the different edge modes of the A-Pf order can account for this discrepancy. The identification of the topological order is crucial for the interpretation of braiding (interference) operations, better understanding of the thermal equilibration process, and the reliability of the numerical studies. We developed a new method that helps identifying the topological order of the ν=5/2 state. By creating an interface between the two 2D half-planes, one hosting the ν=5/2 state and the other an integer ν=3 state, the interface supported a fractional ν=1/2 charge mode with 1/2 quantum conductance and a neutral Majorana mode. The presence of the Majorana mode, probed by measuring noise, propagating in the opposite direction to the charge mode, asserted the presence of the PH-Pf order but not that of the A-Pf order. △ Less

Submitted 5 January, 2021; originally announced January 2021.

Comments: 36 pages, 4 main figures, supplementary data

Journal ref: Science 375, 193-197 (2022)

Superconducting fractional quantum Hall edges via repulsive interactions

Authors: Barak A. Katzir, Ady Stern, Erez Berg, Netanel H. Lindner

Abstract: We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupli… ▽ More We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupling to the superconductor is weak an energy gap is opened only in the presence of sufficiently strong attractive interactions between the edge modes, which do not commonly occur in solid state experimental realizations. We therefore investigate the possibility of obtaining a gapped phase by increasing the strength of the proximity coupling to the superconductor. To this end, we use an effective wire construction model for the quantum Hall liquid and employ renormalization group methods to obtain the phase diagram of the system. Surprisingly, at strong proximity coupling we find a gapped phase which is stabilized for sufficiently strong repulsive interactions in the bulk of the quantum Hall fluids. We furthermore identify a duality transformation that maps between the weak coupling and strong coupling regimes, and use it to show that the gapped phases in both regimes are continuously connected through an intermediate proximity coupling regime. △ Less

Submitted 27 November, 2020; originally announced November 2020.

Comments: 24 pages, 12 figures