Showing 1–50 of 65 results for author: Hyart, T

Transport effects of twist-angle disorder in mesoscopic twisted bilayer graphene

Authors: Aleksander Sanjuan Ciepielewski, Jakub Tworzydło, Timo Hyart, Alexander Lau

Abstract: Magic-angle twisted bilayer graphene is a tunable material with remarkably flat energy bands near the Fermi level, leading to fascinating transport properties and correlated states at low temperatures. However, grown pristine samples of this material tend to break up into landscapes of twist-angle domains, strongly influencing the physical properties of each individual sample. This poses a signifi… ▽ More Magic-angle twisted bilayer graphene is a tunable material with remarkably flat energy bands near the Fermi level, leading to fascinating transport properties and correlated states at low temperatures. However, grown pristine samples of this material tend to break up into landscapes of twist-angle domains, strongly influencing the physical properties of each individual sample. This poses a significant problem to the interpretation and comparison between measurements obtained from different samples. In this work, we study numerically the effects of twist-angle disorder on quantum electron transport in mesoscopic samples of magic-angle twisted bilayer graphene. We find a significant property of twist-angle disorder that distinguishes it from onsite-energy disorder: it leads to an asymmetric broadening of the energy-resolved conductance. The magnitude of the twist-angle variation has a strong effect on conductance, while the number of twist-angle domains is of much lesser significance. We further establish a relationship between the asymmetric broadening and the asymmetric density of states of twisted bilayer graphene at angles smaller than the first magic angle. Our results show that the qualitative differences between the types of disorder in the energy-resolved conductance of twisted bilayer graphene samples can be used to characterize them at temperatures above the critical temperatures of the correlated phases, enabling systematic experimental studies of the effects of the different types of disorders also on the other properties such as the competition of the different types of correlated states appearing at lower temperatures. △ Less

Submitted 28 March, 2024; originally announced March 2024.

Comments: 8 pages, 7 figures

Geometric and conventional contributions to superfluid weight in the minimal models for superconducting copper-doped lead apatite

Authors: Wojciech Brzezicki, Timo Hyart

Abstract: The density functional theory calculations and tight-binding models for the copper-doped lead apatite support flat bands, which could be susceptible to the emergence of high-temperature superconductivity. We develop theory for the geometric contribution of the superfluid weight arising from the momentum-space topology of the Bloch wave functions of these flat bands, and we compare our results to t… ▽ More The density functional theory calculations and tight-binding models for the copper-doped lead apatite support flat bands, which could be susceptible to the emergence of high-temperature superconductivity. We develop theory for the geometric contribution of the superfluid weight arising from the momentum-space topology of the Bloch wave functions of these flat bands, and we compare our results to the paradigmatic case of $s$-wave superconductivity on an isolated topological flat band. We show that, in contrast to the standard paradigm of flat-band superconductivity, there does not exist any lower bound for the superfluid weight in these models. Moreover, although the nontrivial quantum geometries of the normal state bands are the same when the superconductivity appears in the ferromagnetic and paramagnetic phases, the emerging superconducting phases have very different superfluid weights. In the case of superconductivity appearing on the spin-polarized bands the superfluid weight varies a lot as a function of model parameters. On the other hand, if the superconductivity emerges in the paramagnetic phase the superfluid weight is robustly large and it contains a significant geometric component. △ Less

Submitted 25 August, 2023; originally announced August 2023.

Comments: 12 pages, 8 figures

Non-Hermitian topological quantum states in a reservoir-engineered transmon chain

Authors: Wojciech Brzezicki, Matti Silveri, Marcin Płodzień, Francesco Massel, Timo Hyart

Abstract: Dissipation in open systems enriches the possible symmetries of the Hamiltonians beyond the Hermitian framework allowing the possibility of novel non-Hermitian topological phases, which exhibit long-living end states that are protected against disorder. So far, non-Hermitian topology has been explored only in settings where probing genuine quantum effects has been challenging. We theoretically sho… ▽ More Dissipation in open systems enriches the possible symmetries of the Hamiltonians beyond the Hermitian framework allowing the possibility of novel non-Hermitian topological phases, which exhibit long-living end states that are protected against disorder. So far, non-Hermitian topology has been explored only in settings where probing genuine quantum effects has been challenging. We theoretically show that a non-Hermitian topological quantum phase can be realized in a reservoir-engineered transmon chain. The spatial modulation of dissipation is obtained by coupling each transmon to a quantum circuit refrigerator allowing in-situ tuning of dissipation strength in a wide range. By solving the many-body Lindblad master equation using a combination of the density matrix renormalization group and third quantization approaches, we show that the topological end modes and the associated phase transition are visible in simple reflection measurements with experimentally realistic parameters. Finally, we demonstrate that genuine quantum effects are observable in this system via robust and slowly decaying long-range quantum entanglement of the topological end modes, which can be generated passively starting from a locally excited transmon. △ Less

Submitted 6 October, 2022; originally announced October 2022.

Comments: 17 pages, 6 figures

Unprotected edge modes in quantum spin Hall insulator candidate materials

Authors: Nguyen Minh Nguyen, Giuseppe Cuono, Rajibul Islam, Carmine Autieri, Timo Hyart, Wojciech Brzezicki

Abstract: The experiments in quantum spin Hall insulator candidate materials, such as HgTe/CdTe and InAs/GaSb heterostructures, indicate that in addition to the topologically protected helical edge modes these multilayer heterostructures may also support additional edge states, which can contribute to the scattering and the transport. We use first-principles calculations to derive an effective tight-binding… ▽ More The experiments in quantum spin Hall insulator candidate materials, such as HgTe/CdTe and InAs/GaSb heterostructures, indicate that in addition to the topologically protected helical edge modes these multilayer heterostructures may also support additional edge states, which can contribute to the scattering and the transport. We use first-principles calculations to derive an effective tight-binding model for HgTe/CdTe, HgS/CdTe and InAs/GaSb heterostructures, and we show that all these materials support additional edge states which are sensitive to the edge termination. We trace the microscopic origin of these states back to a minimal model supporting flat bands with a nontrivial quantum geometry that gives rise to polarization charges at the edges. We show that the polarization charges transform into the additional edge states when the flat bands are coupled to each other and to the other states to form the Hamiltonian describing the full heterostructure. Interestingly, in the HgTe/CdTe quantum wells the additional edge states are far away from the Fermi level so that they do not contribute to the transport but in the HgS/CdTe and InAs/GaSb heterostructures they appear within the bulk energy gap giving rise to the possibility of multimode edge transport. Finally, we demonstrate that because these additional edge modes are non-topological it is possible to remove them from the bulk energy gap by modifying the edge potential for example with the help of a side gate or chemical doping. △ Less

Submitted 14 September, 2022; originally announced September 2022.

Comments: 11 pages, 9 figures

Transport signatures of Van Hove singularities in mesoscopic twisted bilayer graphene

Authors: Aleksander Sanjuan Ciepielewski, Jakub Tworzydło, Timo Hyart, Alexander Lau

Abstract: Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with Van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surfac… ▽ More Magic-angle twisted bilayer graphene exhibits quasi-flat low-energy bands with Van Hove singularities close to the Fermi level. These singularities play an important role in the exotic phenomena observed in this material, such as superconductivity and magnetism, by amplifying electronic correlation effects. In this work, we study the correspondence of four-terminal conductance and the Fermi surface topology as a function of the twist angle, pressure, and energy in mesoscopic, ballistic samples of small-angle twisted bilayer graphene. We establish a correspondence between features in the wide-junction conductance and the presence of van Hove singularities in the density of states. Moreover, we identify additional transport features, such as a large, pressure-tunable minimal conductance, conductance peaks coinciding with non-singular band crossings, and unusually large conductance oscillations as a function of the system size. Our results suggest that twisted bilayer graphene close the magic angle is a unique system featuring simultaneously large conductance due to the quasi-flat bands, strong quantum nonlinearity due to the Van Hove singularities and high sensitivity to external parameters, which could be utilized in high-frequency device applications and sensitive detectors. △ Less

Submitted 7 December, 2022; v1 submitted 17 August, 2022; originally announced August 2022.

Comments: 9 pages + one page Appendix, contains link to data repository

Journal ref: Phys. Rev. Research 4, 043145 (2022)

Effects of electron-electron interactions in the Yu-Shiba-Rusinov lattice model

Authors: Valerii Kachin, Teemu Ojanen, Jose L. Lado, Timo Hyart

Abstract: In two-dimensional superconductors, Yu-Shiba-Rusinov bound states, induced by the magnetic impurities, extend over long distances giving rise to a long-range hopping model supporting a large number of topological phases with distinct Chern numbers. Here, we study how the electron-electron interactions affect on a mean-field level the selection of the realized Chern numbers and the magnitudes of th… ▽ More In two-dimensional superconductors, Yu-Shiba-Rusinov bound states, induced by the magnetic impurities, extend over long distances giving rise to a long-range hopping model supporting a large number of topological phases with distinct Chern numbers. Here, we study how the electron-electron interactions affect on a mean-field level the selection of the realized Chern numbers and the magnitudes of the topological energy gaps in this model. We find that in the case of an individual choice of the model parameters the interactions can enhance or reduce the topological gap as well as cause topological phase transitions because of the complex interplay of superconductivity, magnetism, and large spatial extent of the Yu-Shiba-Rusinov states. By sampling a large number of realizations of Yu-Shiba-Rusinov lattice models with different model parameters, we show that statistically the interactions have no effect on the realized Chern numbers and typical magnitudes of the topological gaps. However, the interactions substantially increase the likelihood of the largest topological gaps in the tails of the energy gap distribution in comparison to the non-interacting case. △ Less

Submitted 13 August, 2022; originally announced August 2022.

Journal ref: Phys. Rev. B 107, 174522 (2023)

Quantized spin pumping in topological ferromagnetic-superconducting nanowires

Authors: V. Fernández Becerra, Mircea Trif, Timo Hyart

Abstract: Semiconducting nanowires with strong spin-orbit coupling in the presence of induced superconductivity and ferromagnetism can support Majorana zero modes. We study the pumping due to the precession of the magnetization in single-subband nanowires and show that spin pumping is robustly quantized when the hybrid nanowire is in the topologically nontrivial phase, whereas charge pumping is not quantize… ▽ More Semiconducting nanowires with strong spin-orbit coupling in the presence of induced superconductivity and ferromagnetism can support Majorana zero modes. We study the pumping due to the precession of the magnetization in single-subband nanowires and show that spin pumping is robustly quantized when the hybrid nanowire is in the topologically nontrivial phase, whereas charge pumping is not quantized. Moreover, there exists one-to-one correspondence between the quantized conductance, entropy change and spin pumping in long topologically nontrivial nanowires but these observables are uncorrelated in the case of accidental zero-energy Andreev bound states in the trivial phase. Thus, we conclude that observation of correlated and quantized peaks in the conductance, entropy change and spin pumping would provide strong evidence of Majorana zero modes, and we elaborate how topological Majorana zero modes can be distinguished from quasi-Majorana modes potentially created by a smooth tunnel barrier at the lead-nanowire interface. Finally, we discuss peculiar interference effects affecting the spin pumping in short nanowires at very low energies. △ Less

Submitted 1 July, 2023; v1 submitted 7 June, 2022; originally announced June 2022.

Comments: Final version. Modifications in main text (5 pages) and new sections in supplement (11 pages)

Journal ref: Phys. Rev. Lett. 130, 237002 (2023)

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers II: Zero-field topological superconductivity

Authors: Tania Paul, V. Fernández Becerra, Timo Hyart

Abstract: It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here, we show that in the presence of proximity-induced superconductivity it is possible to realize Majorana zero modes in the time-reversal… ▽ More It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here, we show that in the presence of proximity-induced superconductivity it is possible to realize Majorana zero modes in the time-reversal symmetry broken phase in the absence of magnetic field. We develop an effective low-energy theory for the system in the presence of time-reversal symmetry breaking order parameter to obtain analytically the Majorana zero modes and we find a good agreement between the numerical and analytical results in the limit of weakly broken time-reversal symmetry. We show that the Majorana zero modes can be detected in superconductor/time-reversal symmetry broken insulator/superconductor Josephson junctions through the measurement of a $4π$ Josephson current. Finally, we demonstrate that the Majorana fusion-rule detection is feasible by utilizing the gate voltage dependence of the spontaneous time-reversal symmetry breaking order parameter. △ Less

Submitted 26 May, 2022; originally announced May 2022.

Journal ref: Phys. Rev. B 106, 235421 (2022)

Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers I: Transport properties

Authors: Tania Paul, V. Fernández Becerra, Timo Hyart

Abstract: The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron… ▽ More The band-inverted electron-hole bilayers, such as InAs/GaSb, are an interesting playground for the interplay of quantum spin Hall effect and correlation effects because of the small density of electrons and holes and the relatively small hybridization between the electron and hole bands. It has been proposed that Coulomb interactions lead to a time-reversal symmetry broken phase when the electron and hole densities are tuned from the trivial to the quantum spin Hall insulator regime. We show that the transport properties of the system in the time-reversal symmetry broken phase are consistent with the recent experimental observations in InAs/GaSb. Moreover, we carry out a quantum transport study on a Corbino disc where the bulk and edge contributions to the conductance can be separated. We show that the edge becomes smoothly conducting and the bulk is always insulating when one tunes the system from the trivial to the quantum spin Hall insulator phase, providing unambiguous transport signatures of the time-reversal symmetry broken phase. △ Less

Submitted 25 May, 2022; originally announced May 2022.

Journal ref: Phys. Rev. B 106, 235420 (2022)

Universal suppression of superfluid weight by disorder independent of quantum geometry and band dispersion

Authors: Alexander Lau, Sebastiano Peotta, Dmitry I. Pikulin, Enrico Rossi, Timo Hyart

Abstract: Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geom… ▽ More Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor. △ Less

Submitted 2 March, 2022; originally announced March 2022.

Comments: 5 pages + Supplemental Material, contains link to data repository

Journal ref: SciPost Phys. 13, 086 (2022)

Identifying Chern numbers of superconductors from local measurements

Authors: Paul Baireuther, Marcin Płodzień, Teemu Ojanen, Jakub Tworzydło, Timo Hyart

Abstract: Fascination in topological materials originates from their remarkable response properties and exotic quasiparticles which can be utilized in quantum technologies. In particular, large-scale efforts are currently focused on realizing topological superconductors and their Majorana excitations. However, determining the topological nature of superconductors with current experimental probes is an outst… ▽ More Fascination in topological materials originates from their remarkable response properties and exotic quasiparticles which can be utilized in quantum technologies. In particular, large-scale efforts are currently focused on realizing topological superconductors and their Majorana excitations. However, determining the topological nature of superconductors with current experimental probes is an outstanding challenge. This shortcoming has become increasingly pressing due to rapidly developing designer platforms which are theorized to display very rich topology and are better accessed by local probes rather than transport experiments. We introduce a robust machine-learning protocol for classifying the topological states of two-dimensional (2D) chiral superconductors and insulators from local density of states (LDOS) data. Since the LDOS can be measured with standard experimental techniques, our protocol contributes to overcoming the almost three decades standing problem of identifying the topological phase of 2D superconductors with broken time-reversal symmetry. △ Less

Submitted 27 May, 2023; v1 submitted 13 December, 2021; originally announced December 2021.

Comments: 12 pages, 10 figures; v2: revised computer experiments, updated both text and figures

Observation of the Dissipative Parametric Gain in a GaAs/AlGaAs Superlattice

Authors: Vladislovas Čižas, Liudvikas Subačius, Natalia V. Alexeeva, Dalius Seliuta, Timo Hyart, Klaus Köhler, Kirill N. Alekseev, Gintaras Valušis

Abstract: Parametric generation of oscillations and waves is a paradigm, which is known to be realized in various physical systems. Unique properties of quantum superlattices allow to investigate high-frequency phenomena induced by the Bragg reflections and negative differential velocity of the miniband electrons. Effects of parametric gain in the superlattices at different strengths of dissipation have bee… ▽ More Parametric generation of oscillations and waves is a paradigm, which is known to be realized in various physical systems. Unique properties of quantum superlattices allow to investigate high-frequency phenomena induced by the Bragg reflections and negative differential velocity of the miniband electrons. Effects of parametric gain in the superlattices at different strengths of dissipation have been earlier discussed in a number of theoretical works, but their experimental demonstrations are so far absent. Here, we report on the first observation of the dissipative parametric generation in a subcritically doped GaAs/AlGaAs superlattice subjected to a dc bias and a microwave pump. We argue that the dissipative parametric mechanism originates from a periodic variation of the negative differential velocity. It enforces excitation of slow electrostatic waves in the superlattice which provide a significant enhancement of the gain coefficient. This work paves the way for a development of a miniature solid-state parametric generator of GHz\nobreakdash--THz frequencies operating at room temperature. △ Less

Submitted 8 April, 2022; v1 submitted 15 November, 2021; originally announced November 2021.

Comments: The main body includes 6 pages and 3 figures. Supplementary files include 10 pages, 7 figures, and 2 tables

Non-Hermitian many-body topological excitations in interacting quantum dots

Authors: Timo Hyart, Jose L. Lado

Abstract: Quantum dots are one of the paradigmatic solid-state systems for quantum engineering, providing an outstanding tunability to explore fundamental quantum phenomena. Here we show that non-Hermitian many-body topological modes can be realized in a quantum dot chain by utilizing a gate-tunable modulation of dissipation, and they emerge purely because of the non-Hermiticity. By exactly solving the non-… ▽ More Quantum dots are one of the paradigmatic solid-state systems for quantum engineering, providing an outstanding tunability to explore fundamental quantum phenomena. Here we show that non-Hermitian many-body topological modes can be realized in a quantum dot chain by utilizing a gate-tunable modulation of dissipation, and they emerge purely because of the non-Hermiticity. By exactly solving the non-Hermitian interacting description both with exact diagonalization and tensor-networks, we demonstrate that these topological modes are robust even in the presence strong interactions, leading to a strongly correlated topological many-particle state. Our results put forward quantum dot arrays as a platform for engineering non-Hermitian many-body topological modes, and highlight the resilience of non-Hermitian topology to electronic interactions. △ Less

Submitted 29 June, 2021; originally announced June 2021.

Journal ref: Phys. Rev. Research 4, L012006 (2022)

Yu-Shiba-Rusinov qubit

Authors: Archana Mishra, Pascal Simon, Timo Hyart, Mircea Trif

Abstract: Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states which hold a promise for topological quantum computing. However, this ambitious goal looks distant since no quantum coherent degrees of freedom have yet been identified in these sy… ▽ More Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states which hold a promise for topological quantum computing. However, this ambitious goal looks distant since no quantum coherent degrees of freedom have yet been identified in these systems. To fill this gap we propose an effective two-level system, a YSR qubit, stemming from two nearby impurities. Using a time-dependent wave-function approach, we derive an effective Hamiltonian describing the YSR qubit evolution as a function of distance between the impurity spins, their relative orientations, and their dynamics. We show that the YSR qubit can be controlled and read out using the state-of-the-art experimental techniques for manipulation of the spins. Finally, we address the effect of the spin noises on the coherence properties of the YSR qubit, and show a robust behaviour for a wide range of experimentally relevant parameters. Looking forward, the YSR qubit could facilitate the implementation of a universal set of quantum gates in hybrid systems where they are coupled to topological Majorana qubits. △ Less

Submitted 11 December, 2021; v1 submitted 2 June, 2021; originally announced June 2021.

Comments: 23 pages, 7 figures

Journal ref: PRX Quantum 2, 040347 (2021)

Corner states, hinge states and Majorana modes in SnTe nanowires

Authors: Nguyen Minh Nguyen, Wojciech Brzezicki, Timo Hyart

Abstract: SnTe materials are one of the most flexible material platforms for exploring the interplay of topology and different types of symmetry breaking. We study symmetry-protected topological states in SnTe nanowires in the presence of various combinations of Zeeman field, s-wave superconductivity and inversion-symmetry-breaking field. We uncover the origin of robust corner states and hinge states in the… ▽ More SnTe materials are one of the most flexible material platforms for exploring the interplay of topology and different types of symmetry breaking. We study symmetry-protected topological states in SnTe nanowires in the presence of various combinations of Zeeman field, s-wave superconductivity and inversion-symmetry-breaking field. We uncover the origin of robust corner states and hinge states in the normal state. In the presence of superconductivity, we find inversion-symmetry-protected gapless bulk Majorana modes, which give rise to quantized thermal conductance in ballistic wires. By introducing an inversion-symmetry-breaking field, the bulk Majorana modes become gapped and topologically protected localized Majorana zero modes appear at the ends of the wire. △ Less

Submitted 28 February, 2022; v1 submitted 24 May, 2021; originally announced May 2021.

Comments: 16 pages, 13 figures

Journal ref: Phys. Rev. B 105, 075310 (2022)

Tunable topological states hosted by unconventional superconductors with adatoms

Authors: Andreas Kreisel, Timo Hyart, Bernd Rosenow

Abstract: Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic… ▽ More Chains of magnetic atoms, placed on the surface of s-wave superconductors, have been established as a laboratory for the study of Majorana bound states. In such systems, the breaking of time reversal due to magnetic moments gives rise to the formation of in-gap states, which hybridize to form one-dimensional topological superconductors. However, in unconventional superconductors even non-magnetic impurities induce in-gap states since scattering of Cooper pairs changes their momentum but not their phase. Here, we propose a path for creating topological superconductivity, which is based on an unconventional superconductor with a chain of non-magnetic adatoms on its surface. The topological phase can be reached by tuning the magnitude and direction of a Zeeman field, such that Majorana zero modes at its boundary can be generated, moved and fused. To demonstrate the feasibility of this platform, we develop a general mapping of films with adatom chains to one-dimensional lattice Hamiltonians. This allows us to study unconventional superconductors such as Sr$_2$RuO$_4$ exhibiting multiple bands and an anisotropic order parameter. △ Less

Submitted 15 July, 2021; v1 submitted 24 February, 2021; originally announced February 2021.

Comments: 8 pages, 4 figures, including supplemental material (published version)

Journal ref: Phys. Rev. Research 3, 033049 (2021)

Topological valley currents via ballistic edge modes in graphene superlattices near the primary Dirac point

Authors: Yang Li, Mario Amado, Timo Hyart, Grzegorz P. Mazur, Jason W. A. Robinson

Abstract: Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but… ▽ More Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities based on the Landauer-Büttiker formalism show evidence for spin-degenerate ballistic valley-helical edge modes, which are key for the development of valleytronics △ Less

Submitted 17 December, 2020; originally announced December 2020.

Journal ref: Communications Physics, 3, 224 (2020)

Topological charge, spin and heat transistor

Authors: V. Fernández Becerra, Mircea Trif, Timo Hyart

Abstract: Spin pumping consists in the injection of spin currents into a non-magnetic material due to the precession of an adjacent ferromagnet. In addition to the pumping of spin the precession always leads to pumping of heat, but in the presence of spin-orbital entanglement it also leads to a charge current. We investigate the pumping of charge, spin and heat in a device where a superconductor and a quant… ▽ More Spin pumping consists in the injection of spin currents into a non-magnetic material due to the precession of an adjacent ferromagnet. In addition to the pumping of spin the precession always leads to pumping of heat, but in the presence of spin-orbital entanglement it also leads to a charge current. We investigate the pumping of charge, spin and heat in a device where a superconductor and a quantum spin Hall insulator are in proximity contact with a ferromagnetic insulator. We show that the device supports two robust operation regimes arising from topological effects. In one regime, the pumped charge, spin and heat are quantized and related to each other due to a topological winding number of the reflection coefficient in the scattering matrix formalism -- translating to a Chern number in the case of Hamiltonian formalism. In the second regime, a Majorana zero mode switches off the pumping of currents owing to the topologically protected perfect Andreev reflection. We show that the interplay of these two topological effects can be utilized so that the device operates as a robust charge, spin and heat transistor. △ Less

Submitted 10 June, 2021; v1 submitted 3 December, 2020; originally announced December 2020.

Comments: Final accepted version

Journal ref: Phys. Rev. B 103, 205410 (2021)

Many-body Majorana-like zero modes without gauge symmetry breaking

Authors: V. Vadimov, T. Hyart, J. L. Lado, M. Möttönen, T. Ala-Nissila

Abstract: Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting one-dimensional many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-… ▽ More Topological superconductors represent one of the key hosts of Majorana-based topological quantum computing. Typical scenarios for one-dimensional topological superconductivity assume a broken gauge symmetry associated to a superconducting state. However, no interacting one-dimensional many-body system is known to spontaneously break gauge symmetries. Here, we show that zero modes emerge in a many-body system without gauge symmetry breaking and in the absence of superconducting order. In particular, we demonstrate that Majorana zero modes of the symmetry-broken superconducting state are continuously connected to these zero-mode excitations, demonstrating that zero-bias anomalies may emerge in the absence of gauge symmetry breaking. We demonstrate that these many-body zero modes share the robustness features of the Majorana zero modes of symmetry-broken topological superconductors. We introduce a bosonization formalism to analyze these excitations and show that a ground state analogous to a topological superconducting state can be analytically found in a certain limit. Our results demonstrate that robust Majorana-like zero modes may appear in a many-body systems without gauge symmetry breaking, thus introducing a family of protected excitations with no single-particle analogs. △ Less

Submitted 12 November, 2020; originally announced November 2020.

Journal ref: Phys. Rev. Research 3, 023002 (2021)

Designing three-dimensional flat bands in nodal-line semimetals

Authors: Alexander Lau, Timo Hyart, Carmine Autieri, Anffany Chen, Dmitry I. Pikulin

Abstract: Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in t… ▽ More Electrons with large kinetic energy have a superconducting instability for infinitesimal attractive interactions. Quenching the kinetic energy and creating a flat band renders an infinitesimal repulsive interaction the relevant perturbation. Thus, flat band systems are an ideal platform to study the competition of superconductivity and magnetism and their possible coexistence. Recent advances in the field of twisted bilayer graphene highlight this in the context of two-dimensional materials. Two dimensions, however, put severe restrictions on the stability of the low-temperature phases due to enhanced fluctuations. Only three-dimensional flat bands can solve the conundrum of combining the exotic flat-band phases with stable order existing at high temperatures. Here, we present a way to generate such flat bands through strain engineering in topological nodal-line semimetals. We present analytical and numerical evidence for this scenario and study the competition of the arising superconducting and magnetic orders as a function of externally controlled parameters. We show that the order parameter is rigid because the quantum geometry of the Bloch wave functions leads to a large superfluid stiffness. Using density-functional theory and numerical tight-binding calculations we further apply our theory to strained rhombohedral graphite and CaAgP materials. △ Less

Submitted 26 March, 2021; v1 submitted 20 August, 2020; originally announced August 2020.

Comments: 8 pages + Appendix, contains link to data repository. v2: change of title, extended introduction and discussion, two new sections in the Appendix

Journal ref: Phys. Rev. X 11, 031017 (2021)

Quantum-metric-enabled exciton condensate in double twisted bilayer graphene

Authors: Xiang Hu, Timo Hyart, Dmitry I. Pikulin, Enrico Rossi

Abstract: Flat-band systems are a promising platform for realizing exotic collective ground states with spontaneously broken symmetry because the electron-electron interactions dominate over the kinetic energy. A collective ground state of particular interest is the chased after exciton condensate (EC). However, in flat band systems other collective ground states can compete with an EC phase, and the conven… ▽ More Flat-band systems are a promising platform for realizing exotic collective ground states with spontaneously broken symmetry because the electron-electron interactions dominate over the kinetic energy. A collective ground state of particular interest is the chased after exciton condensate (EC). However, in flat band systems other collective ground states can compete with an EC phase, and the conventional treatment of the effect of thermal and quantum fluctuations predicts the EC phase should be unstable. Here, using double twisted bilayer graphene (TBLG) heterostructures as an example, we show that for realistic interaction strengths the EC phase is favored with respect to other TBLG's phases -- orbital magnetism and superconductivity -- when the TBLGs have opposite doping, and that the quantum metric of the Bloch wave functions stabilizes the EC, reversing the conclusion that would be drawn from the conventional approach in which quantum metric contributions are neglected. Our results suggest that the quantum metric plays a critical role in determining the stability of exciton condensates in double layers formed by systems with flat-bands. △ Less

Submitted 19 April, 2022; v1 submitted 7 August, 2020; originally announced August 2020.

Comments: 6 pages, 6 figures

Journal ref: Phys. Rev. B 105, L140506 (2022)

Signatures of dephasing by mirror-symmetry breaking in weak-antilocalization magnetoresistance across the topological transition in Pb$_{1-x}$Sn$_{x}$Se

Authors: Alexander Kazakov, Wojciech Brzezicki, Timo Hyart, Bartłomiej Turowski, Jakub Polaczyński, Zbigniew Adamus, Marta Aleszkiewicz, Tomasz Wojciechowski, Jaroslaw Z. Domagala, Ondrej Caha, Andrei Varykhalov, Gunther Springholz, Tomasz Wojtowicz, Valentine V. Volobuev, Tomasz Dietl

Abstract: Many conductors, including recently studied Dirac materials, show saturation of coherence length on decreasing temperature. This surprising phenomenon is assigned to external noise, residual magnetic impurities or two-level systems specific to non-crystalline solids. Here, by considering the SnTe-class of compounds as an example, we show theoretically that breaking of mirror symmetry deteriorates… ▽ More Many conductors, including recently studied Dirac materials, show saturation of coherence length on decreasing temperature. This surprising phenomenon is assigned to external noise, residual magnetic impurities or two-level systems specific to non-crystalline solids. Here, by considering the SnTe-class of compounds as an example, we show theoretically that breaking of mirror symmetry deteriorates Berry's phase quantization, leading to additional dephasing in weak-antilocalization magnetoresistance (WAL-MR). Our experimental studies of WAL-MR corroborate these theoretical expectations in (111) Pb$_{1-x}$Sn$_x$Se thin film with Sn contents $x$ corresponding to both topological crystalline insulator and topologically trivial phases. In particular, we find the shortening of the phase coherence length in samples with intentionally broken mirror symmetry. Our results indicate that the classification of quantum transport phenomena into universality classes should encompass, in addition to time-reversal and spin-rotation invariances, spatial symmetries in specific systems. △ Less

Submitted 21 June, 2021; v1 submitted 18 February, 2020; originally announced February 2020.

Comments: Accepted version

Journal ref: Phys. Rev. B 103, 245307 (2021)

Non-Hermitian Topological End-Mode Lasing in Polariton Systems

Authors: Paolo Comaron, Vanik Shahnazaryan, Wojciech Brzezicki, Timo Hyart, Michał Matuszewski

Abstract: We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to {\it enforced exceptional… ▽ More We predict the existence of non-Hermitian topologically protected end states in a one-dimensional exciton-polariton condensate lattice, where topological transitions are driven by the laser pump pattern. We show that the number of end states can be described by a Chern number and a topological invariant based on the Wilson loop. We find that such transitions arise due to {\it enforced exceptional points} which can be predicted directly from the bulk Bloch wave functions. This allows us to establish a new type of bulk-boundary correspondence for non-Hermitian systems and to compute the phase diagram of an open chain analytically. Finally, we demonstrate topological lasing of a single end-mode in a realistic model of a microcavity lattice. △ Less

Submitted 15 June, 2020; v1 submitted 13 December, 2019; originally announced December 2019.

Comments: Main text (6 pages) and Supplementary Material (4 pages)

Journal ref: Phys. Rev. Research 2, 022051 (2020)

Hidden Chern number in one-dimensional non-Hermitian chiral-symmetric systems

Authors: Wojciech Brzezicki, Timo Hyart

Abstract: We consider a class of one-dimensional non-Hermitian models with a special type of a chiral symmetry which is related to pseudo-Hermiticity. We show that the topology of a Hamiltonian belonging to this symmetry class is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian $H^{\rm eff} (k, η)$, where $η$ is the imaginary part of the energy. This Chern number manife… ▽ More We consider a class of one-dimensional non-Hermitian models with a special type of a chiral symmetry which is related to pseudo-Hermiticity. We show that the topology of a Hamiltonian belonging to this symmetry class is determined by a hidden Chern number described by an effective 2D Hermitian Hamiltonian $H^{\rm eff} (k, η)$, where $η$ is the imaginary part of the energy. This Chern number manifests itself as topologically protected in-gap end states at zero real part of the energy. We show that the bulk-boundary correspondence coming from the hidden Chern number is robust and immune to non-Hermitian skin effect. We introduce a minimal model Hamiltonian supporting topologically nontrivial phases in this symmetry class, derive its topological phase diagram and calculate the end states originating from the hidden Chern number. △ Less

Submitted 9 October, 2019; v1 submitted 5 August, 2019; originally announced August 2019.

Comments: 8 pages, 8 figures

Journal ref: Phys. Rev. B 100, 161105 (2019)

Topological domain wall states in a non-symmorphic chiral chain

Authors: Wojciech Brzezicki, Timo Hyart

Abstract: The Su-Schrieffer-Heeger (SSH) model, containing dimerized hopping and a constant onsite energy, has become a paradigmatic model for one-dimensional topological phases, soliton excitations and fractionalized charge in the presence of chiral symmetry. Motivated by the recent developments in engineering artificial lattices, we study an alternative model where hopping is constant but the onsite energ… ▽ More The Su-Schrieffer-Heeger (SSH) model, containing dimerized hopping and a constant onsite energy, has become a paradigmatic model for one-dimensional topological phases, soliton excitations and fractionalized charge in the presence of chiral symmetry. Motivated by the recent developments in engineering artificial lattices, we study an alternative model where hopping is constant but the onsite energy is dimerized. We find that it has a non-symmorphic chiral symmetry and supports topologically distinct phases described by a $\mathbb{Z}_{2}$ invariant $ν$. In the case of multimode ribbon we also find topological phases protected by hidden symmetries and we uncover the corresponding $\mathbb{Z}_{2}$ invariants $ν_{n}$. We show that, in contrast to the SSH case, zero-energy states do not necessarily appear at the boundary between topologically distinct phases, but instead these systems support a new kind of bulk-boundary correspondence: The energy of the topological domain wall states typically scales to zero as $1/w$, where $w$ is the width of the domain wall separating phases with different topology. Moreover, under specific circumstances we also find a faster scaling $e^{-w/ξ}$, where $ξ$ is an intrinsic length scale. We show that the spectral flow of these states and the charge of the domain walls are different than in the case of the SSH model. △ Less

Submitted 5 June, 2020; v1 submitted 25 July, 2019; originally announced July 2019.

Comments: 11 pages, 7 figures

Journal ref: Phys. Rev. B 101, 235113 (2020)

Geometric and conventional contribution to superfluid weight in twisted bilayer graphene

Authors: Xiang Hu, Timo Hyart, Dmitry I. Pikulin, Enrico Rossi

Abstract: By tuning the angle between graphene layers to specific "magic angles" the lowest energy bands of twisted bilayer graphene (TBLG) can be made flat. The flat nature of the bands favors the formation of collective ground states and, in particular, TBLG has been shown to support superconductivity. When the energy bands participating in the superconductivity are well-isolated, the superfluid weight sc… ▽ More By tuning the angle between graphene layers to specific "magic angles" the lowest energy bands of twisted bilayer graphene (TBLG) can be made flat. The flat nature of the bands favors the formation of collective ground states and, in particular, TBLG has been shown to support superconductivity. When the energy bands participating in the superconductivity are well-isolated, the superfluid weight scales inversely with the effective mass of such bands. For flat-band systems one would therefore conclude that even if superconducting pairing is present most of the signatures of the superconducting state should be absent. This conclusion is at odds with the experimental observations for TBLG. We calculate the superfluid weight for TBLG taking into account both the conventional contribution and the contribution arising from the quantum geometry of the bands. We find that both contributions are larger than one would expect treating the bands as well-isolated, that at the magic angle the geometric contribution is larger than the conventional one, and that for small deviations away from the magic angle the conventional contribution is larger than the geometric one. Our results show that, despite the flatness of the bands the superfluid weight in TBLG is finite and consistent with experimental observations. We also show how the superfluid weight can be tuned by varying the chemical potential and the twist angle opening the possibility to tune the nature of the superconducting transition between the standard BCS transition and the Berezinskii-Kosterlitz-Thouless transition. △ Less

Submitted 5 December, 2019; v1 submitted 17 June, 2019; originally announced June 2019.

Comments: 6 pages, 6 figures

Journal ref: Phys. Rev. Lett. 123, 237002 (2019)

Transition between canted antiferromagnetic and spin-polarized ferromagnetic quantum Hall states in graphene on a ferrimagnetic insulator

Authors: Y. Li, M. Amado, T. Hyart, G. P. Mazur, V. Risinggård, T. Wagner, L. McKenzie Sell, G. Kimbell, J. Wunderlich, J. Linder, J. W. A. Robinson

Abstract: In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$.… ▽ More In the quantum Hall regime of graphene, antiferromagnetic and spin-polarized ferromagnetic states at the zeroth Landau level compete, leading to a canted antiferromagnetic state depending on the direction and magnitude of an applied magnetic field. Here, we investigate this transition at 2.7 K in graphene Hall bars that are proximity coupled to the ferrimagnetic insulator Y$_{3}$Fe$_{5}$O$_{12}$. From nonlocal transport measurements, we demonstrate an induced magnetic exchange field in graphene, which lowers the magnetic field required to modulate the magnetic state in graphene. These results show that a magnetic proximity effect in graphene is an important ingredient for the development of two-dimensional materials in which it is desirable for ordered states of matter to be tunable with relatively small applied magnetic fields (> 6 T). △ Less

Submitted 1 June, 2020; v1 submitted 16 May, 2019; originally announced May 2019.

Comments: 25 pages, 17 figures

Journal ref: Phys. Rev. B 101, 241405 (2020)

Moiré with flat bands is different

Authors: Tero T. Heikkila, Timo Hyart

Abstract: Recent experimental discoveries of superconductivity and other exotic electronic states in twisted bilayer graphene (TBG) call for a reconsideration of our traditional theories of these states, usually based on the assumption of the presence of a Fermi surface. Here we show how such developments may even help us finding mechanisms of increasing the critical temperature of superconductivity towards… ▽ More Recent experimental discoveries of superconductivity and other exotic electronic states in twisted bilayer graphene (TBG) call for a reconsideration of our traditional theories of these states, usually based on the assumption of the presence of a Fermi surface. Here we show how such developments may even help us finding mechanisms of increasing the critical temperature of superconductivity towards the room temperature. △ Less

Submitted 2 May, 2019; v1 submitted 30 April, 2019; originally announced April 2019.

Comments: Feature article submitted to Europhysics News. Added another paper in Ref. 2

Journal ref: Europhys. News 50, 24 (2019)

Machine learning assisted measurement of local topological invariants

Authors: Marcello D. Caio, Marco Caccin, Paul Baireuther, Timo Hyart, Michel Fruchart

Abstract: The continuous effort towards topological quantum devices calls for an efficient and non-invasive method to assess the conformity of components in different topological phases. Here, we show that machine learning paves the way towards non-invasive topological quality control. To do so, we use a local topological marker, able to discriminate between topological phases of one-dimensional wires. The… ▽ More The continuous effort towards topological quantum devices calls for an efficient and non-invasive method to assess the conformity of components in different topological phases. Here, we show that machine learning paves the way towards non-invasive topological quality control. To do so, we use a local topological marker, able to discriminate between topological phases of one-dimensional wires. The direct observation of this marker in solid state systems is challenging, but we show that an artificial neural network can learn to approximate it from the experimentally accessible local density of states. Our method distinguishes different non-trivial phases, even for systems where direct transport measurements are not available and for composite systems. This new approach could find significant use in experiments, ranging from the study of novel topological materials to high-throughput automated material design. △ Less

Submitted 23 January, 2019; v1 submitted 10 January, 2019; originally announced January 2019.

Topological properties of multilayers and surface steps in the SnTe material class

Authors: Wojciech Brzezicki, Marcin Wysokiński, Timo Hyart

Abstract: Surfaces of multilayer semiconductors typically have regions of atomically flat terraces separated by atom-high steps. Here we investigate the properties of the low-energy states appearing at the surface atomic steps in \snte. We identify the important approximate symmetries and use them to construct relevant topological invariants. We calculate the dependence of mirror- and spin-resolved Chern nu… ▽ More Surfaces of multilayer semiconductors typically have regions of atomically flat terraces separated by atom-high steps. Here we investigate the properties of the low-energy states appearing at the surface atomic steps in \snte. We identify the important approximate symmetries and use them to construct relevant topological invariants. We calculate the dependence of mirror- and spin-resolved Chern numbers on the number of layers and show that the step states appear when these invariants are different on the two sides of the step. Moreover, we find that a particle-hole symmetry can protect one-dimensional Weyl points at the steps. Since the local density of states is large at the step the system is susceptible to different types of instabilities, and we consider an easy-axis magnetization as one realistic possibility. We show that magnetic domain walls support low-energy bound states because the regions with opposite magnetization are topologically distinct in the presence of non-symmorphic chiral and mirror symmetries, providing a possible explanation for the zero-bias conductance peak observed in the recent experiment [Mazur et al., Phys. Rev. B 100, 041408(R) (2019)] △ Less

Submitted 17 September, 2019; v1 submitted 5 December, 2018; originally announced December 2018.

Journal ref: Phys. Rev. B 100, 121107 (2019)

Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band

Authors: R. Ojajärvi, T. Hyart, M. Silaev, T. T. Heikkilä

Abstract: The effective attractive interaction between electrons, mediated by electron-phonon coupling, is a well-established mechanism of conventional superconductivity. In metals exhibiting a Fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Therefore such superconductors are found only at temperatures below a few Kelvin. Systems w… ▽ More The effective attractive interaction between electrons, mediated by electron-phonon coupling, is a well-established mechanism of conventional superconductivity. In metals exhibiting a Fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Therefore such superconductors are found only at temperatures below a few Kelvin. Systems with flat energy bands have been suggested to cure the problem and provide a route to room-temperature superconductivity, but previous studies are limited to only BCS models with an effective attractive interaction. Here we generalize Eliashberg's theory of strong-coupling superconductivity to systems with flat bands and relate the mean-field critical temperature to the microscopic parameters describing electron-phonon and electron-electron interaction. We also analyze the strong-coupling corrections to the BCS results, and construct the phase diagram exhibiting superconductivity and magnetic phases on an equal footing. Our results are especially relevant for novel quantum materials where electronic dispersion and interaction strength are controllable. △ Less

Submitted 30 November, 2018; v1 submitted 5 January, 2018; originally announced January 2018.

Journal ref: Phys. Rev. B 98, 054515 (2018)

Two topologically distinct Dirac-line semimetal phases and topological phase transitions in rhombohedrally stacked honeycomb lattices

Authors: T. Hyart, R. Ojajärvi, T. T. Heikkilä

Abstract: Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a… ▽ More Three-dimensional topological semimetals can support band crossings along one-dimensional curves in the momentum space (nodal lines or Dirac lines) protected by structural symmetries and topology. We consider rhombohedrally (ABC) stacked honeycomb lattices supporting Dirac lines protected by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model. △ Less

Submitted 13 December, 2017; v1 submitted 15 September, 2017; originally announced September 2017.

Journal ref: J. Low Temp. Phys. (2018)

Robust semi-Dirac points and unconventional topological phase transitions in doped superconducting Sr2IrO4 tunnel coupled to t2g electron systems

Authors: Mats Horsdal, Timo Hyart

Abstract: Semi-Dirac fermions are known to exist at the critical points of topological phase transitions requiring fine-tuning of the parameters. We show that robust semi-Dirac points can appear in a heterostructure consisting of superconducting Sr2IrO4 and a t2g electron system (t2g-ES) without fine-tuning. They are topologically stable in the presence of the symmetries of the model, metallic t2g-ES and a… ▽ More Semi-Dirac fermions are known to exist at the critical points of topological phase transitions requiring fine-tuning of the parameters. We show that robust semi-Dirac points can appear in a heterostructure consisting of superconducting Sr2IrO4 and a t2g electron system (t2g-ES) without fine-tuning. They are topologically stable in the presence of the symmetries of the model, metallic t2g-ES and a single active band in Sr2IrO4. If the t2g metal is coupled to two different layers of Sr2IrO4 (effectively a multiband superconductor) in a three-layer-structure the semi-Dirac points can split into two stable Dirac points with opposite chiralities. A similar transition can be achieved if the t2g-ES supports intrinsic triplet superconductivity. By considering Sr2RuO4 as an example of a t2g-ES we predict a rich topological phase diagram as a function of various parameters. △ Less

Submitted 11 January, 2018; v1 submitted 8 May, 2017; originally announced May 2017.

Comments: Published version

Journal ref: SciPost Phys. 3, 041 (2017)

Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

Authors: T. Hyart, T. T. Heikkila

Abstract: Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for Helium-3. Close to the nexus the Dirac lines exhibit a transition from ty… ▽ More Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each other, forming a momentum-space equivalent of the real-space nexus considered before for Helium-3. Close to the nexus the Dirac lines exhibit a transition from type I to type II lines. We consider a general model of stacked honeycomb lattices with the symmetry of Bernal (AB) stacked graphite and show that the structural mirror symmetries in such systems protect the presence of the Dirac lines, and also naturally lead to the formation of the nexus. By the bulk-boundary correspondence of topological media, the presence of Dirac lines lead to the formation of drumhead surface states at the side surfaces of the system. We calculate the surface state spectrum, and especially illustrate the effect of the nexus on these states. △ Less

Submitted 27 June, 2016; v1 submitted 21 April, 2016; originally announced April 2016.

Journal ref: Phys. Rev. B 93, 235147 (2016)

Mapping an electron wave function by a local electron scattering probe

Authors: Christian Reichl, Werner Dietsche, Thomas Tschirky, Timo Hyart, Werner Wegscheider

Abstract: A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to 15E6 cm^2/Vs. Thin ("delta") layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the… ▽ More A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to 15E6 cm^2/Vs. Thin ("delta") layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the Al "delta"-layer. By changing the distance of this layer from the interface we map the shape of the wave function perpendicular to the interface. Despite having a profound effect on the electron mobiliy, the "delta"-layers do not cause a widening of the quantum Hall plateaus. △ Less

Submitted 27 October, 2015; originally announced October 2015.

Comments: 15 pages, five figures

Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

Authors: Lukas Kimme, Timo Hyart

Abstract: We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalize… ▽ More We consider the effects of impurities on topological insulators and superconductors. We start by identifying the general conditions under which the eigenenergies of an arbitrary Hamiltonian H belonging to one of the Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a function of an external parameter which can be, for example, the impurity strength. We define a generalized root of \det H, and use it to predict or rule out robust zero-energy crossings in all symmetry classes. We complement this result with an analysis based on almost degenerate perturbation theory, which allows a derivation of the asymptotic low-energy behavior of the ensemble averaged density of states $ρ\sim E^α$ for all symmetry classes, and makes it transparent that the exponent α does not depend on the choice of the random matrix ensemble. Finally, we show that a lattice of impurities can drive a topologically trivial system into a nontrivial phase, and in particular we demonstrate that impurity bands carrying extremely large Chern numbers can appear in different symmetry classes of two-dimensional topological insulators and superconductors. We use the generalized root of \det H(k) to reveal a spiderweblike momentum space structure of the energy gap closings that separate the topologically distinct phases in p_x + i p_y superconductors in the presence of an impurity lattice. △ Less

Submitted 26 January, 2016; v1 submitted 20 October, 2015; originally announced October 2015.

Comments: 13 pages, 13 figures, 1 table; published version (minor revisions of the text, references added)

Journal ref: Phys. Rev. B 93, 035134 (2016)

Collective amplitude mode fluctuations in a flat band superconductor

Authors: V. J. Kauppila, T. Hyart, T. T. Heikkilä

Abstract: We study the fluctuations of the amplitude (i.e. the Higgs-Anderson) mode in a superconducting system of coupled Dirac particles proposed as a model for possible surface or interface superconductivity in rhombohedral graphite. We show that the absence of Fermi energy and vanishing of the excitation gap of the collective amplitude mode in the model leads to a large fluctuation contribution to therm… ▽ More We study the fluctuations of the amplitude (i.e. the Higgs-Anderson) mode in a superconducting system of coupled Dirac particles proposed as a model for possible surface or interface superconductivity in rhombohedral graphite. We show that the absence of Fermi energy and vanishing of the excitation gap of the collective amplitude mode in the model leads to a large fluctuation contribution to thermodynamic quantities such as the heat capacity. As a consequence, the mean-field theory becomes inaccurate indicating that the interactions lead to a strongly correlated state. We also present a microscopic derivation of the Ginzburg-Landau theory corresponding to this model. △ Less

Submitted 12 May, 2015; v1 submitted 11 May, 2015; originally announced May 2015.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 93, 024505 (2016)

Confinement-deconfinement transition due to spontaneous symmetry breaking in quantum Hall bilayers

Authors: D. I. Pikulin, P. G. Silvestrov, T. Hyart

Abstract: Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. In contrast to the chiral edge states of the quantum Hall exciton condensate in electron-electron bilayers, existence of the… ▽ More Band-inverted electron-hole bilayers support quantum spin Hall insulator and exciton condensate phases. We investigate such a bilayer in an external magnetic field. We show that the interlayer correlations lead to formation of a helical quantum Hall exciton condensate state. In contrast to the chiral edge states of the quantum Hall exciton condensate in electron-electron bilayers, existence of the counterpropagating edge modes results in formation of a ground state spin-texture not supporting gapless single-particle excitations. This feature has deep consequences for the low energy behavior of the system. Namely, the charged edge excitations in a sufficiently narrow Hall bar are confined, i.e.~a charge on one of the edges always gives rise to an opposite charge on the other edge. Moreover, we show that magnetic field and gate voltages allow to control confinement-deconfinement transition of charged edge excitations, which can be probed with nonlocal conductance. Confinement-deconfinement transitions are of great interest, not least because of their possible significance in shedding light on the confinement problem of quarks. △ Less

Submitted 13 October, 2015; v1 submitted 20 April, 2015; originally announced April 2015.

Comments: 19 pages, 8 figures; v3: added Landau level diagrams and discussion of quantization breakdown

Journal ref: Nature Communications, 7, 10462 (2016)

Physical Principles of the Amplification of Electromagnetic Radiation Due to Negative Electron Masses in a Semiconductor Superlattice

Authors: A. V. Shorokhov, M. A. Pyataev, N. N. Khvastunov, T. Hyart, F. V. Kusmartsev, K. N. Alekseev

Abstract: In a superlattice placed in crossed electric and magnetic fields, under certain conditions, the inversion of electron population can appear at which the average energy of electrons is above the middle of the miniband and the effective mass of the electron is negative. This is the implementation of the negative effective mass amplifier and generator (NEMAG) in the superlattice. It can result in the… ▽ More In a superlattice placed in crossed electric and magnetic fields, under certain conditions, the inversion of electron population can appear at which the average energy of electrons is above the middle of the miniband and the effective mass of the electron is negative. This is the implementation of the negative effective mass amplifier and generator (NEMAG) in the superlattice. It can result in the amplification and generation of terahertz radiation even in the absence of negative differential conductivity. △ Less

Submitted 16 March, 2015; originally announced March 2015.

Comments: 5 pages, 3 figures

Journal ref: JETP Letters, Volume 100, Issue 12, pp 766-770 (2014)

Enhancing triplet superconductivity by the proximity to a singlet superconductor in oxide heterostructures

Authors: Mats Horsdal, Giniyat Khaliullin, Timo Hyart, Bernd Rosenow

Abstract: We show how in principle a coherent coupling between two superconductors of opposite parity can be realized in a three-layer oxide heterostructure. Due to strong intraionic spin-orbit coupling in the middle layer, singlet Cooper pairs are converted into triplet ones and vice versa. This results in a large enhancement of the triplet superconductivity, persisting well above the native triplet critic… ▽ More We show how in principle a coherent coupling between two superconductors of opposite parity can be realized in a three-layer oxide heterostructure. Due to strong intraionic spin-orbit coupling in the middle layer, singlet Cooper pairs are converted into triplet ones and vice versa. This results in a large enhancement of the triplet superconductivity, persisting well above the native triplet critical temperature. △ Less

Submitted 7 June, 2016; v1 submitted 9 January, 2015; originally announced January 2015.

Comments: Minor improvements, references added, published version. 5 pages, 3 figures

Journal ref: Phys. Rev. B 93, 220502 (2016)

Giant negative magnetoresistance driven by spin-orbit coupling at the LAO/STO interface

Authors: M. Diez, A. M. R. V. L. Monteiro, G. Mattoni, E. Cobanera, T. Hyart, E. Mulazimoglu, N. Bovenzi, C. W. J. Beenakker, A. D. Caviglia

Abstract: The LAO/STO interface hosts a two-dimensional electron system that is unusually sensitive to the application of an in-plane magnetic field. Low-temperature experiments have revealed a giant negative magnetoresistance (dropping by 70\%), attributed to a magnetic-field induced transition between interacting phases of conduction electrons with Kondo-screened magnetic impurities. Here we report on exp… ▽ More The LAO/STO interface hosts a two-dimensional electron system that is unusually sensitive to the application of an in-plane magnetic field. Low-temperature experiments have revealed a giant negative magnetoresistance (dropping by 70\%), attributed to a magnetic-field induced transition between interacting phases of conduction electrons with Kondo-screened magnetic impurities. Here we report on experiments over a broad temperature range, showing the persistence of the magnetoresistance up to the 20~K range --- indicative of a single-particle mechanism. Motivated by a striking correspondence between the temperature and carrier density dependence of our magnetoresistance measurements we propose an alternative explanation. Working in the framework of semiclassical Boltzmann transport theory we demonstrate that the combination of spin-orbit coupling and scattering from finite-range impurities can explain the observed magnitude of the negative magnetoresistance, as well as the temperature and electron density dependence. △ Less

Submitted 18 May, 2015; v1 submitted 17 December, 2014; originally announced December 2014.

Comments: new updates from feedback and review process. main text: improved discussion of the mechanisms of the MR; a discussion of a rescaling of the MR with a characteristic field B*(n). supplemental: theoretical estimate of the "sweet spot" density and window; effect of an out-of-plane B-field component on the MR; discussion of spin-orbit corrections to Boltzmann transport. 6+4 pages, 4+4 figures

Journal ref: Phys. Rev. Lett. 115, 016803 (2015)

Andreev-Bragg reflection from an Amperian superconductor

Authors: P. Baireuther, T. Hyart, B. Tarasinski, C. W. J. Beenakker

Abstract: We show how an electrical measurement can detect the pairing of electrons on the same side of the Fermi surface (Amperian pairing), recently proposed by Patrick Lee for the pseudogap phase of high-$T_c$ cuprate superconductors. Bragg scattering from the pair-density wave introduces odd multiples of $2k_{\rm F}$ momentum shifts when an electron incident from a normal metal is Andreev-reflected as a… ▽ More We show how an electrical measurement can detect the pairing of electrons on the same side of the Fermi surface (Amperian pairing), recently proposed by Patrick Lee for the pseudogap phase of high-$T_c$ cuprate superconductors. Bragg scattering from the pair-density wave introduces odd multiples of $2k_{\rm F}$ momentum shifts when an electron incident from a normal metal is Andreev-reflected as a hole. These Andreev-Bragg reflections can be detected in a three-terminal device, containing a ballistic Y-junction between normal leads $(1,2)$ and the superconductor. The cross-conductance $dI_1/dV_2$ has the opposite sign for Amperian pairing than it has either in the normal state or for the usual BCS pairing. △ Less

Submitted 14 March, 2015; v1 submitted 9 September, 2014; originally announced September 2014.

Comments: 5 pages, 6 figures; v2 includes study of disorder and interface barrier

Journal ref: Phys. Rev. Lett. 115, 097001 (2015)

Minimal circuit for a flux-controlled Majorana qubit in a quantum spin-Hall insulator

Authors: B. van Heck, T. Hyart, C. W. J. Beenakker

Abstract: We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux… ▽ More We construct a minimal circuit, based on the top-transmon design, to rotate a qubit formed out of four Majorana zero-modes at the edge of a two-dimensional topological insulator. Unlike braiding operations, generic rotations have no topological protection, but they do allow for a full characterization of the coherence times of the Majorana qubit. The rotation is controlled by variation of the flux through a pair of split Josephson junctions in a Cooper pair box, without any need to adjust gate voltages. The Rabi oscillations of the Majorana qubit can be monitored via oscillations in the resonance frequency of the microwave cavity that encloses the Cooper pair box. △ Less

Submitted 10 July, 2014; originally announced July 2014.

Comments: Contribution for the proceedings of the Nobel Symposium on topological insulators. 8 pages, 6 figures

Journal ref: Phys. Scr. T164, 014007 (2015)

Zeeman field induced topological phase transitions in triplet superconductors

Authors: Timo Hyart, Anthony R. Wright, Bernd Rosenow

Abstract: We develop a general Ginzburg-Landau theory which describes the effect of a Zeeman field on the superconducting order parameter in triplet superconductors. Starting from Ginzburg-Landau theories that describe fully gapped time-reversal symmetric triplet superconductors, we show that the Zeeman field has dramatic effects on the topological properties of the superconductors. In particular, in the vi… ▽ More We develop a general Ginzburg-Landau theory which describes the effect of a Zeeman field on the superconducting order parameter in triplet superconductors. Starting from Ginzburg-Landau theories that describe fully gapped time-reversal symmetric triplet superconductors, we show that the Zeeman field has dramatic effects on the topological properties of the superconductors. In particular, in the vicinity of a critical chemical potential separating two topologically distinct phases, it is possible to induce a phase transition to a topologically nontrivial phase which supports chiral edge modes. Moreover, for specific directions of the Zeeman field, we obtain nodal superconducting phases with an emerging chiral symmetry, and with Majorana flat bands at the edge. The Ginzburg-Landau theory is microscopically supported by a self-consistent mean-field theory of the doped Kitaev-Heisenberg model. △ Less

Submitted 16 May, 2014; originally announced May 2014.

Disorder and magnetic-field induced breakdown of helical edge conduction in an inverted electron-hole bilayer

Authors: D. I. Pikulin, T. Hyart, Shuo Mi, J. Tworzydło, M. Wimmer, C. W. J. Beenakker

Abstract: We calculate the conductance of a two-dimensional bilayer with inverted electron-hole bands, to study the sensitivity of the quantum spin Hall insulator (with helical edge conduction) to the combination of electrostatic disorder and a perpendicular magnetic field. The characteristic breakdown field for helical edge conduction splits into two fields with increasing disorder, a field $B_{c}$ for the… ▽ More We calculate the conductance of a two-dimensional bilayer with inverted electron-hole bands, to study the sensitivity of the quantum spin Hall insulator (with helical edge conduction) to the combination of electrostatic disorder and a perpendicular magnetic field. The characteristic breakdown field for helical edge conduction splits into two fields with increasing disorder, a field $B_{c}$ for the transition into a quantum Hall insulator (supporting chiral edge conduction) and a smaller field $B'_{c}$ for the transition to bulk conduction in a quasi-metallic regime. The spatial separation of the inverted bands, typical for broken-gap InAs/GaSb quantum wells, is essential for the magnetic-field induced bulk conduction --- there is no such regime in HgTe quantum wells. △ Less

Submitted 30 April, 2014; v1 submitted 1 January, 2014; originally announced January 2014.

Comments: 4 pages, 6 figures; Corrected a factor of two error in the magnetic field scale and effective g-factor

Journal ref: Phys. Rev. B 89, 161403(R) (2014)

Interplay of exciton condensation and quantum spin Hall effect in InAs/GaSb bilayers

Authors: D. I. Pikulin, T. Hyart

Abstract: We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For small tunneling amplitude between the layers, we find that the system is prone to formation of an s-wave exciton condensate phase, where the spin-structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and doe… ▽ More We study the phase diagram of the inverted InAs/GaSb bilayer quantum wells. For small tunneling amplitude between the layers, we find that the system is prone to formation of an s-wave exciton condensate phase, where the spin-structure of the order parameter is uniquely determined by the small spin-orbit coupling arising from the bulk inversion asymmetry. The phase is topologically trivial and does not support edge transport. On the contrary, for large tunneling amplitude, we obtain a topologically non-trivial quantum spin Hall insulator phase with a p-wave exciton order parameter, which enhances the hybridization gap. These topologically distinct insulators are separated by an insulating phase with spontaneously broken time-reversal symmetry. Close to the phase transition between the quantum spin Hall and time-reversal broken phases, the edge transport shows quantized conductance in small samples, whereas in long samples the mean free path associated with the backscattering at the edge is temperature independent, in agreement with recent experiments. △ Less

Submitted 18 May, 2014; v1 submitted 5 November, 2013; originally announced November 2013.

Comments: v. 2, 9 pages, 5 figures

Journal ref: Phys. Rev. Lett. 112, 176403 (2014)

Symmetry-protected topological invariant and Majorana impurity states in time-reversal-invariant superconductors

Authors: Lukas Kimme, Timo Hyart, Bernd Rosenow

Abstract: We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal-invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength. These symmetries allow the definition of a position-space topological Z_2 invariant, which is related to the standard bu… ▽ More We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal-invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength. These symmetries allow the definition of a position-space topological Z_2 invariant, which is related to the standard bulk topological Z_2 invariant. Our general results are applied to the time-reversal-invariant p-wave phase of the doped Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can drive a topologically trivial system into the nontrivial phase. △ Less

Submitted 2 June, 2015; v1 submitted 12 August, 2013; originally announced August 2013.

Comments: published version

Journal ref: Phys. Rev. B 91, 220501 (2015)

Effects of disorder on Coulomb-assisted braiding of Majorana zero modes

Authors: I. C. Fulga, B. van Heck, M. Burrello, T. Hyart

Abstract: Majorana zero modes in one-dimensional topological superconductors obey non-Abelian braiding statistics. Braiding manipulations can be realized by controlling Coulomb couplings in hybrid Majorana-transmon devices. However, strong disorder may induce accidental Majorana modes, which are expected to have detrimental effects on braiding statistics. Nevertheless, we show that the Coulomb-assisted brai… ▽ More Majorana zero modes in one-dimensional topological superconductors obey non-Abelian braiding statistics. Braiding manipulations can be realized by controlling Coulomb couplings in hybrid Majorana-transmon devices. However, strong disorder may induce accidental Majorana modes, which are expected to have detrimental effects on braiding statistics. Nevertheless, we show that the Coulomb-assisted braiding protocol is efficiently realized also in the presence of accidental modes. The errors occurring during the braiding cycle are small if the couplings of the computational Majorana modes to the accidental ones are much weaker than the maximum Coulomb coupling. △ Less

Submitted 29 October, 2013; v1 submitted 1 August, 2013; originally announced August 2013.

Comments: 7 pages, 4 figures, this is the final, published version

Journal ref: Phys. Rev. B 88, 155435 (2013)

Superfluid Stiffness of a Driven Dissipative Condensate with Disorder

Authors: Alexander Janot, Timo Hyart, Paul R. Eastham, Bernd Rosenow

Abstract: Observations of macroscopic quantum coherence in driven systems, e.g. polariton condensates, have strongly stimulated experimental as well as theoretical efforts during the last decade. We address the question of whether a driven quantum condensate is a superfluid, allowing for the effects of disorder and its non-equilibrium nature. We predict that for spatial dimensions d<4 the superfluid stiffne… ▽ More Observations of macroscopic quantum coherence in driven systems, e.g. polariton condensates, have strongly stimulated experimental as well as theoretical efforts during the last decade. We address the question of whether a driven quantum condensate is a superfluid, allowing for the effects of disorder and its non-equilibrium nature. We predict that for spatial dimensions d<4 the superfluid stiffness vanishes once the condensate exceeds a critical size, and treat in detail the case d=2. Thus a non-equilibrium condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems. △ Less

Submitted 11 December, 2013; v1 submitted 4 July, 2013; originally announced July 2013.

Comments: 5 pages, 5 figures

Journal ref: Phys. Rev. Lett. 111, 230403 (2013)

Flux-controlled quantum computation with Majorana fermions

Authors: T. Hyart, B. van Heck, I. C. Fulga, M. Burrello, A. R. Akhmerov, C. W. J. Beenakker

Abstract: Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by e… ▽ More Majorana fermions hold promise for quantum computation, because their non-Abelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of well-separated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully flux-controlled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initialization--braiding--measurement steps required to demonstrate non-Abelian statistics. We introduce the Random Access Majorana Memory, a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multi-qubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits. △ Less

Submitted 29 July, 2013; v1 submitted 18 March, 2013; originally announced March 2013.

Comments: Final version

Journal ref: Phys. Rev. B 88, 035121 (2013)