The Quantum Spin Hall Effect: Theory and Experiment

Abstract

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Recently, a new class of topological insulators has been proposed. These topological insulators have an insulating gap in the bulk, but have topologically protected edge states due to the time reversal symmetry. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the band structure changes from a normal to an "inverted" type at a critical thickness $d_c$. We present an analytical solution of the helical edge states and explicitly demonstrate their topological stability. We also review the recent experimental observation of the QSH state in HgTe/(Hg,Cd)Te quantum wells. We review both the fabrication of the sample and the experimental setup. For thin quantum wells with well width $d_{QW}<6.3$ nm, the insulating regime shows the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells ($d_{QW}>6.3$ nm), the nominally insulating regime shows a plateau of residual conductance close to $2e^2/h$. The residual conductance is independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance is destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, $d_c=6.3$ nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition.

Invited review article for special issue of JPSJ, 32 pages. For higher resolution figures see official online version when published

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Cited by in corpus (487)

• Topological Insulators
• Topological insulators and superconductors
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• Classification of topological quantum matter with symmetries
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
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• Model Hamiltonian for Topological Insulators
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Three-Dimensional Topological Insulators
• Topological Anderson Insulator
• Chiral Topological Superconductor From the Quantum Hall State
• Spin dynamics in semiconductors
• Inversion Symmetric Topological Insulators
• The Zak phase and the existence of edge states in graphene
• Manipulation of Majorana fermion, Andreev reflection and Josephson current on topological insulators
• Topological Phases in Two-Dimensional Materials: A Brief Review
• Finite size effects of helical edge states in HgTe/CdTe quantum wells
• Theory of the topological Anderson insulator
• Splitting of a Cooper pair by a pair of Majorana bound states
• Unconventional superconductivity on a topological insulator
• Observation of Quantum Spin Hall States in InAs/GaSb Bilayers under Broken Time-Reversal Symmetry
• Induced Superconductivity in the Quantum Spin Hall Edge
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• Anomalous Finite Size Effects on Surface States in the Topological Insulator Bi${}_2$Se${}_3$
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Topological Nature of the Phonon Hall Effect
• Spin polarization of the quantum spin Hall edge states
• Single valley Dirac fermions in zero-gap HgTe quantum wells
• Random-matrix theory of Majorana fermions and topological superconductors
• Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells
• Imaging currents in HgTe quantum wells in the quantum spin Hall regime
• Disorder-induced Floquet Topological Insulators
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Majorana edge states in interacting one-dimensional systems
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• Landau quantization and the thickness limit of topological insulator thin films of Sb2Te3
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• Dynamical preparation of Floquet Chern insulators
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• Imaging Quantum Spin Hall Edges in Monolayer WTe2
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• Quantum Spin Hall Effect in Two-dimensional Crystals of Transition Metal Dichalcogenides
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• Theoretical Prediction of Topological Insulators in Thallium-based III-V-VI${}_2$ Ternary Chalcogenides
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• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• K-Theory and Pseudospectra for Topological Insulators
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• Critical Behavior of a Point Contact in a Quantum Spin Hall Insulator
• Interplay between Superconductivity and Ferromagnetism on a Topological Insulator
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• Topological states in two-dimensional optical lattices
• Type-II Ising Pairing in Few-Layer Stanene
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• Transport in disordered two-dimensional topological insulator
• Resistance of helical edges formed in a semiconductor heterostructure
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Reconfigurable Topological Photonic Crystal
• Topological and geometrical aspects of band theory
• Quantum Anomalous Hall Effect with Cold Atoms Trapped in a Square Lattice
• Introduction to Dirac materials and topological insulators
• Topological Insulators and C^*-Algebras: Theory and Numerical Practice
• The dependence of topological Anderson insulator on the type of disorder
• Weak antilocalization in HgTe quantum wells and topological surface states: Massive versus massless Dirac fermions
• Intrinsic conduction through topological surface states of insulating Bi${}_2$Te${}_3$ epitaxial thin films
• Topological insulator: a new quantized spin Hall resistance robust to dephasing
• Full electrical control of Charge and Spin conductance through Interferometry of Edge States in Topological Insulators
• Spatially resolved study of backscattering in the quantum spin Hall state
• The translational side of topological band insulators
• Helical Luttinger liquid in topological insulator nanowires
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• Spin Texture in a Cold Exciton Gas
• Spin currents in a coherent exciton gas
• Pressure and temperature driven phase transitions in HgTe quantum wells
• Spin-helical transport in normal and superconducting topological insulators
• Magnetoconductance of the quantum spin Hall state
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• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Topological equivalence of crystal and quasicrystal band structures
• Torsion, Parity-odd Response and Anomalies in Topological States
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• Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
• Localization and Mobility Gap in Topological Anderson Insulator
• Split Dirac cones in HgTe/CdTe quantum wells due to symmetry-enforced level anticrossing at interfaces
• Novel Spin-texture on the warped Dirac-cone surface states in topological insulators
• Ballistic quantum spin Hall state and enhanced edge backscattering in strong magnetic fields
• Magnetic properties of HgTe quantum wells
• Quantum Spin Hall Effect in Strip of Stripes Model
• Atomically Thin Quantum Spin Hall Insulators
• Spontaneous breakdown of topological protection in two dimensions
• Low-Energy Effective Hamiltonian and the Surface States of Ca_3PbO
• Patterns of Electro-magnetic Response in Topological Semi-metals
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• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Finite-size effects in non-Hermitian topological systems
• Disorder-Induced Multiple Transition involving Z2 Topological Insulator
• Topological states in quasicrystals
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• Spin Aharonov-Bohm effect and topological spin transistor
• Temperature-driven single-valley Dirac fermions in HgTe quantum wells
• Phonon-induced topological insulation
• Magnetic field induced localization in 2D topological insulators
• Topologically Protected Quantum Coherence in a Superatom
• Andreev bound states and current-phase relations in three-dimensional topological insulators
• Quasi-Topological Electromagnetic Response of Line-node Semimetals
• Proximity induced superconductivity in Weyl semi-metals
• Unconventional topological phase transition in two-dimensional systems with space-time inversion symmetry
• Electrically Controlled Pumping of Spin Currents in Topological Insulators
• Magnetotransport of Dirac Fermions on the surface of a topological insulator
• The phonon Hall effect: theory and application
• Spintronics and spincaloritronics in topological insulators
• Mesoscopic fluctuations of conductance of a helical edge contaminated by magnetic impurities
• Finite-size energy gap in weak and strong topological insulators
• Topological insulators in the quaternary chalcogenide compounds and ternary famatinite compounds
• Fractional Topological Insulators: from sliding Luttinger Liquids to Chern-Simons theory
• Spin current and spin accumulation near a Josephson junction between a singlet and triplet superconductor
• Plasmon mass and Drude weight in strongly spin-orbit-coupled 2D electron gases
• Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States
• Testing Topological Protection of Edge States in Hexagonal Quantum Spin Hall Candidate Materials
• Detection of Majorana Kramers pairs using a quantum point contact
• Topological Insulator in the Presence of Spatially Correlated Disorder
• Gate-controlled semimetal-topological insulator transition in an InAs/GaSb heterostructure
• Quench Dynamics of Edge States in 2-D Topological Insulator Ribbons
• Junction between surfaces of two topological insulators
• Linear magnetoresistance in HgTe quantum wells
• Crossover from Majorana edge to end states in quasi-one-dimensional p-wave superconductors
• Robustness of Quantum Spin Hall Effect in an External Magnetic Field
• Bloch-Zener Oscillations in Graphene and Topological Insulators
• Survival of the quantum anomalous Hall effect in orbital magnetic fields as a consequence of the parity anomaly
• High Chern number quantum anomalous Hall phases in graphene ribbons with Haldane orbital coupling
• The Anomalous de Haas-van Alphen Effect in InAs/GaSb quantum wells
• Helical Liquids in Semiconductors
• Spin polarised scanning tunneling probe for helical Luttinger liquids
• Zigzag edge modes in Z2 topological insulator: reentrance and completely flat spectrum
• Chirality blockade of Andreev reflection in a magnetic Weyl semimetal
• Electrically Controlled Spin Injection from Giant Rashba Spin-Orbit Conductor BiTeBr
• Transport through a quantum spin Hall quantum dot
• Anomalous Electron Trajectory in Topological Insulators
• Spectral properties of Luttinger liquids: A comparative analysis of regular, helical, and spiral Luttinger liquids
• Realistic picture of helical edge states in HgTe quantum wells
• Interacting two helical edge modes in quantum spin Hall systems
• Photon dressed electronic states in topological insulators: Tunneling and conductance
• Backscattering in helical edge states from a magnetic impurity and Rashba disorder
• Spin-orbit effects in a graphene bipolar pn junction
• Hyperfine interactions in two-dimensional HgTe topological insulators
• Signatures of Rashba spin-orbit interaction in the superconducting proximity effect in helical Luttinger liquids
• Spin-Hall effect and spin-Coulomb drag in doped semiconductors
• Quantum transport in disordered systems under magnetic fields: A study based on operator algebras
• Circular photogalvanic effect in HgTe/CdHgTe quantum well structures
• The characterization of topological properties in Quantum Monte Carlo simulations of the Kane-Mele-Hubbard model
• Coulomb blockade microscopy of spin density oscillations and fractional charge in quantum spin Hall dots
• Spin current in topologically trivial and nontrivial noncentrosymmetric superconductors
• Probing surface states of topological insulator: Kondo effect and Friedel oscillation under magnetic field
• Magnetic field induced Fabry-Pérot resonances in helical edge states
• Energy spectrum and broken spin-surface locking in topological insulator quantum dots
• The valence band energy spectrum of HgTe quantum wells with inverted band structures
• Electrical manipulation and measurement of spin properties of quantum spin Hall edge states
• Photogalvanic effect in HgTe/CdTe topological insulator due to edge-bulk optical transitions
• Coherent Oscillations and Giant Edge Magnetoresistance in Singly Connected Topological Insulators
• Optical manipulation of edge state transport in HgTe quantum wells in the quantum hall regime
• Quantum Andreev effect in 2D HgTe/CdTe quantum well-superconductor systems
• Spin-dependent thermoelectric transport in HgTe/CdTe quantum wells
• Landau levels, edge states, and strained magnetic waveguides in graphene monolayers with enhanced spin-orbit interaction
• Reentrant topological phases in Mn-doped HgTe quantum wells
• Robust Helical Edge Transport in Quantum Spin Hall Quantum Wells
• Anatomy of Topological Surface States: Exact Solutions from Destructive Interference on Frustrated Lattices
• Quadratic pseudospectrum for identifying localized states
• Design principles for HgTe based topological insulator devices
• Spin current pumping in helical Luttinger liquids
• Tunnel junction of helical edge states: Determining and controlling spin-preserving and spin-flipping processes through transconductance
• Cyclotron resonance of single valley Dirac fermions in gapless HgTe quantum well
• Analytic Theory of Edge Modes in Topological Insulators
• Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements
• Discovery of a hybrid topological quantum state in an elemental solid
• High-frequency nonlinear transport and photogalvanic effects in two-dimensional topological insulators
• Antichiral states in twisted graphene multilayers
• Light-induced phase crossovers in a quantum spin Hall system
• Time-resolved pure spin fractionalization and spin-charge separation in helical Luttinger liquid based devices
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Generic helical edge states due to Rashba spin-orbit coupling in a topological insulator
• Quantum interference in topological insulator Josephson junctions
• Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators
• Engineering quantum spin Hall insulators by strained-layer heterostructures
• Photoexcitation of electron wave packets in quantum spin Hall edge states: effects of chiral anomaly from a localised electric pulse
• Helical edge transport in the presence of a magnetic impurity
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• Exact edge, bulk and bound states of finite topological systems
• Robust Level Coincidences in the Subband Structure of Quasi 2D Systems
• Topological insulators based on HgTe
• Edge states, corner states, and flat bands in a two-dimensional $\mathcal{P}\mathcal{T}$ symmetric system
• Efficient algorithm to compute the second Chern number in four dimensional systems
• Phase-tunable thermal rectification in the topological SQUIPT
• Majorana fermions in s-wave noncentrosymmetric superconductor with Rashba and Dresselhaus (110) spin-orbit couplings
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension
• Spin Chern Pumping from the Bulk of Two-Dimensional Topological Insulators
• Formation and detection of Majorana modes in quantum spin Hall trenches
• Ferromagnetism and quantum anomalous Hall effect in one-side-saturated buckled honeycomb lattices
• Correlation effects in pyrochlore iridate thin films grown along the $[111]$ direction
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• Edge states of a three-dimensional topological insulator
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• Spin Transfer Torque and Electric Current in Helical Edge States in Quantum Spin Hall Devices
• Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator
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• 3D Dynamics of 4D Topological BF Theory With Boundary
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• Edge states in a ferromagnetic honeycomb lattice with armchair boundaries
• Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers
• Chiral Majorana edge states in HgTe quantum wells
• Magnetotransport signatures of three-dimensional topological insulator nanostructures
• Boundary states and Non-Abelian Casimir effect in lattice Yang-Mills theory
• Transport across a junction of topological insulators and a superconductor
• Transport phenomena in helical edge states interferometers. A Green's function approach
• Helical thermoelectrics and refrigeration
• Perspectives of HgTe Topological Insulators for Quantum Hall Metrology
• Interplay of chiral and helical states in a Quantum Spin Hall Insulator lateral junction
• Topological winding properties of spin edge states in Kane-Mele graphene model
• Non-Equilibrium Transport Through a Gate-Controlled Barrier on the Quantum Spin Hall Edge
• Tunneling magnetoresistance devices based on topological insulators: Ferromagnet/insulator/topological-insulator junctions employing Bi${}_2$Se${}_3$
• Transition between ordinary and topological insulator regimes in two-dimensional resonant magnetotransport
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• Helical edge transport in the presence of a magnetic impurity: the role of local anisotropy
• Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions
• Quantum-Hall to Insulator Transition in Ultra-low-carrier-density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level
• The effect of in-plane magnetic field and applied strain in quantum spin Hall systems: application to InAs/GaSb quantum wells
• Edge accumulation and currents of moment in 2D topological insulators
• A Strongly-Interacting Dirac Liquid on the Surface of a Topological Kondo Insulator
• Helical edge states in multiple topological mass domains
• Topology hierarchy of transition metal dichalcogenides built from quantum spin Hall layers
• Zeeman field-induced two-dimensional Weyl semimetal phase in cadmium arsenide
• Mesoscopic spin Hall effect along a potential step in graphene
• Temperature and Chemical Potential Dependence of the Parity Anomaly in Quantum Anomalous Hall Insulators
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Magnetotransport in disordered two-dimensional topological insulators: signatures of charge puddles
• Noise and current correlations in tunnel junctions of Quantum Spin Hall edge states
• Direct manifestation of band topology in the winding number of the Wannier-Stark ladder
• Majorana-like localized spin density without bound states in topologically trivial spin-orbit coupled nanowires
• Gate defined wires in HgTe quantum wells: from Majorana fermions to spintronics
• Quantum anomalous Hall effect and electric-field-induced topological phase transition in AB-stacked MoTe${}_2$/WSe${}_2$ moiré heterobilayers
• Disorder effects in topological insulator thin films
• Magnetotransport in Double Quantum Well with Inverted Energy Spectrum: HgTe/CdHgTe
• The Haldane model under nonuniform strain
• Nonlocal Edge State Transport in Topological Insulators
• Work Extraction and Landauer's Principle in a Quantum Spin Hall Device
• Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells
• Marginal topological properties of graphene: a comparison with topological insulators
• Electronic states induced by nonmagnetic defects in two-dimensional topological insulators
• Spin liquids in graphene
• A new approach to transport coefficients in the quantum spin Hall effect
• Partition Functions and Stability Criteria of Topological Insulators
• Magnonic Su-Schrieffer-Heeger Model in Honeycomb Ferromagnets
• Switching of electrical current by spin precession in the first Landau level of an inverted-gap semiconductor
• Floquet engineering of topological phase transitions in quantum spin Hall $\alpha$-$T_3$ system
• Fate of Quantum Anomalous Hall Effect in the Presence of External Magnetic Fields and Particle-Hole Asymmetry
• Backscattering in a helical liquid induced by Rashba spin-orbit coupling and electron interactions: locality, symmetry, and cutoff aspects
• Unconventional Reentrant Quantum Hall Effect in a HgTe/CdHgTe Double Quantum Well
• Extrinsic anomalous Hall conductivity of a topologically nontrivial conduction band
• Floquet FFLO superfluids and Majorana fermions in a shaken fermionic optical lattice
• Two-dimensional topological insulator edge state backscattering by dephasing
• Percolating States in the Topological Anderson Insulator
• Thermal signature of Majorana fermions in Josephson junction
• Momentum-Space Spin Texture in a Topological Superconductor
• Unconventional Hall effect near charge neutrality point in a two-dimensional electron-hole system
• $\pi$ Spin Berry Phase in a Quantum-Spin-Hall-Insulator-Based Interferometer: Evidence for the Helical Spin Texture of the Edge States
• Phase diagram of two interacting helical states
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• Topological edge state engineering with high-frequency electromagnetic radiation
• Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator
• Theory of edge states based on the hermiticity of tight-binding Hamiltonian operators
• Photoinduced Quantum Anomalous Hall States in the Topological Anderson Insulator
• Transversal Propagation Behaviors of Helical Edge States In a QSH System
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• Finite-size Topology
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• Disorder-induced phase transition in Dirac systems beyond the linear approximation
• Optimizing Topological Switching in Confined 2D-Xene Nanoribbons via Finite-Size Effects
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• Effects of surface-bulk hybridization in 3D topological `metals'
• Optical properties of helical edge channels in zinc-blende-type topological insulators: Selection rules, circular and linear dichroism, circular and linear photocurrents
• Analytical study of the edge states in the bosonic Haldane model
• Gauge theory of topological phases of matter
• Using Topological Insulator Proximity to Generate Perfectly Conducting Channels in Materials without Topological Protection
• Searching for topological density wave insulators in multi-orbital square lattice systems
• Majorana fermions manifested as interface-states in semiconductor hybrid structures
• Interplay of bulk and edge states in transport of two-dimensional topological insulators
• On-chip coherent frequency-domain THz spectroscopy for electrical transport
• Controlling spin polarization of a quantum dot via a helical edge state
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Chiral heat transport in driven quantum Hall and quantum spin Hall edge states
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Synchronous and Asynchronous Mott Transitions in Topological Insulator Ribbons
• Living on the edge: Topology, electrostatics and disorder
• Signature of Phase Transitions in the Disordered Quantum Spin Hall State From the Entanglement Spectrum
• Probing the Band Topology of Mercury Telluride through Weak Localization and Antilocalization
• One-dimensional non-interacting topological insulators with chiral symmetry
• Nonlinear magneto-gyrotropic photogalvanic effect
• Interacting topological mirror excitonic insulator in one dimension
• Topological insulator ring with magnetic impurities
• Coherent Single Spin Source based on topological insulator
• Effects of Spin Polarization in the HgTe Quantum Well
• Bifurcation of the Edge-State Width in the Two-Dimensional Topological Insulator
• Dynamical density and spin response of Fermi arcs and their consequences for Weyl semimetals
• Electric field modulation of topological order in thin film semiconductors
• Proposal for an ac spin current source
• Interference-induced magnetoresistance in HgTe quantum wells
• Synthetic helical liquid in a quantum wire
• Finite frequency backscattering current noise at a helical edge
• Topological cutoff frequency in a slab waveguide: Penetration length in topological insulator walls
• Cooperative orbital moments and edge magnetoresistance in monolayer WTe${}_2$
• Terahertz Magnetospectroscopy of Cyclotron Resonances from Topological Surface States in Thick Films of Cd${}_x$Hg${}_{1-x}$Te
• Effects of disorder on electron tunneling through helical edge states
• Many-particle effects in optical transitions from zero-mode Landau levels in HgTe quantum wells
• Two-dimensional topological insulators in quantizing magnetic fields
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Edge states in the three-quarter filled system, $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Influence of edge magnetization and electric fields on zigzag silicene, germanene and stanene nanoribbons
• Spin-selective localization due to intrinsic spin-orbit coupling
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Elastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities
• Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory
• Interaction induced edge states in HgTe/CdTe Quantum Well under magnetic field
• Edge capacitance of a 2D topological insulator
• Influence of bulk inversion asymmetry on the magneto-optical spectrum of a HgTe topological insulator
• Emergence, evolution, and control of multistability in a hybrid topological quantum/classical system
• Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Finite-temperature conductance of strongly interacting quantum wire with a nuclear spin order
• Topological field-effect transistor with quantized ON/OFF conductance of helical/chiral dislocation states
• Density of states of a dissipative quantum dot coupled to a quantum wire
• Tunable spin-polarized edge transport in inverted quantum-well junctions
• Photoexcitation in two-dimensional topological insulators: Generating and controlling electron wavepackets in Quantum Spin Hall systems
• Analytical Solutions for the Surface States of Bi${}_{1-x}$Sb${}_x$ ($0\le x\lesssim 0.1$)
• Magnetic-field switchable metal-insulator transitions in a quasi-helical conductor
• Ground state of Ce${}_3$Bi${}_4$Pd${}_3$ unraveled by hydrostatic pressure
• Berry Curvature and Bulk-Boundary Correspondence from Transport Measurement for Photonic Chern Bands
• Signature of pressure-induced topological phase transition in ZrTe${}_5$
• Quantum capacitance of an HgTe quantum well as an indicator of the topological phase
• Electromagnetic Response of Three-dimensional Topological Crystalline Insulators
• Effective model for massless Dirac electrons on a surface of weak topological insulators
• Revealing topological Dirac fermions at the surface of strained HgTe thin films via Quantum Hall transport spectroscopy
• Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Persistent currents and spin torque caused by percolated quantum spin Hall state
• Engineering Topological quantum dot through planar magnetization in bismuthene
• Parity symmetry as the origin of 'spin' in the quantum spin Hall effect
• Low-energy effective theory and anomalous Hall effect in monolayer ${\mathrm{WTe}}_2$
• ${\mathbb{Z}}_2$ topological invariants for mixed states of fermions in time-reversal invariant band structures
• Waiting time distributions in Quantum spin hall based heterostructures
• Robustness of Helical Edge States Under Edge Reconstruction
• Synthetic topological Kondo insulator in a pumped optical cavity
• Conductance suppression by nonmagnetic point defects in helical edge channels of two-dimensional topological insulators
• Microwave Photoresistance of a Two-Dimensional Topological Insulator in a HgTe Quantum Well
• Transport through a quantum spin Hall antidot as a spectroscopic probe of spin textures
• Ferromagnetism in armchair graphene nanoribbon heterostructures
• Anomalous Spin Response and Virtual-Carrier-Mediated Magnetism in a Topological Insulator
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Engineering chiral edge states in 2D topological insulator/ferromagnetic insulator heterostructures
• Nonlocal transport in a hybrid two-dimensional topological insulator
• The effect of magnetic impurity scattering on transport in topological insulators
• Spin texture of an irradiated warped topological insulator surface
• Semiclassical electron transport at the edge of a 2D topological insulator: Interplay of protected and unprotected modes
• Wavepacket dynamics on Chern band lattices in a trap
• Electrically controlled crossing of energy levels in quantum dots in two-dimensional topological insulators
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Fraunhofer pattern in the presence of Majorana zero modes
• Multiprobe quantum spin Hall bars
• Quantum interference in HgTe structures
• Topological phases due to the coexistence of superconductivity and spin-density wave: Application to high Tc superconductors in the underdoped regime
• Two dimensional topological insulator in quantizing magnetic fields
• Diffusive transport in the lowest Landau level of disordered 2d semimetals: the mean-square-displacement approach
• Spin-momentum locked modes on anti-phase boundaries in photonic crystals
• Substrate-limited helical edge states
• Helical Edge Modes near Transition to Topological Insulator with Indirect Gap
• Plasmons in single- and double-component helical liquids: Application to two-dimensional topological insulators
• Tunable polarization in beam-splitter based on 2D topological insulators
• Identifying Majorana bound states at quantum spin Hall edges using a metallic probe
• Transport and STM studies of hyperbolic surface states of topological insulators
• Electronic polarization in non-Bloch band theory
• Faraday rotation and transmittance as markers of topological phase transitions in 2D materials
• Néel Spin-Orbit Torque in Antiferromagnetic Quantum Spin and Anomalous Hall Insulators
• Edge supercurrent in Josephson junctions based on topological materials
• Artificial topological models based on a one-dimensional spin-dependent optical lattice
• Stability of Topological Insulators with Non-Abelian Edge Excitations
• Dual topological insulator with mirror symmetry protected helical edge states
• Tuning Majorana zero modes with temperature in $\pi$-phase Josephson junctions
• Efficient algorithm to compute the Berry conductivity
• Spin conductances and magnetization production in chiral molecular junctions
• Topological phase transitions in an inverted InAs/GaSb quantum well driven by tilted magnetic fields
• Interplay between intrinsic and emergent topological protection on interacting helical modes
• Anomalous quantum Hall effect induced by disorder in topological insulators
• Spectrum collapse of disordered Dirac Landau levels as topological non-Hermitian physics
• Dynamics of one-dimensional electrons with broken spin-charge separation
• Splitting of Dirac cones in HgTe quantum wells: Effects of crystallographic orientation, interface-, bulk-, and structure-inversion asymmetry
• Transport in quantum spin Hall edges in contact to a quantum dot
• Weak localization and Berry flux in topological crystalline insulators with a quadratic surface spectrum
• $Z_2$ antiferromagnetic topological insulators with broken $C_4$ symmetry
• A k.p treatment of edge states in narrow 2D topological insulators, with standard boundary conditions for the wave function and its derivative
• Transport signatures of a quantum spin Hall - chiral topological superconductor junction
• Bias-Voltage-Induced Topological Phase Transition in Finite Size Quantum Spin Hall Systems in the Presence of a Transverse Electric Field
• Anomalous photo-thermal effects in multi-layered semi-Dirac black phosphorus
• Long-range perturbation of helical edge states by nonmagnetic defects in two-dimensional topological insulators
• The Dirac paradox in 1+1 dimensions and its realization with spin-orbit coupled nanowires
• Coexistent topological and chiral phonons in chiral RhGe: An ab initio study
• Exact solution for many-body Hamiltonian of interacting particles with linear spectrum
• Optical transitions in two-dimensional topological insulators with point defects
• Experimental realization of Majorana hinge and corner modes in intrinsic organic topological superconductor without magnetic field at room temperature
• Quantum revivals in HgTe/CdTe quantum wells and topological phase transitions
• Role of Hund's splitting in electronic phase competition in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$
• Condensates in double-well potential with synthetic gauge potentials and vortex seeding
• Electronic states, pseudo-spin, and transport in the zinc-blende quantum wells and wires with vanishing band gap
• Effects of electron-hole asymmetry on electronic structure of helical edge states in HgTe/HgCdTe quantum wells
• Dynamics of Anderson localization in disordered wires
• Reentrant quantum spin Hall effect in the presence of an exchange field
• Optical N-plasmon: Topological hydrodynamic excitations in Graphene from repulsive Hall viscosity
• Magnetotransport properties of the Quantum Spin Hall and Quantum Hall states in an inverted HgTe/CdTe and InAs/GaSb quantum wells
• Quantum spin compass models in 2D electronic topological metasurfaces
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Charged impurity scattering in two-dimensional topological insulators with Mexican-hat dispersion
• Harmonic generation in bent graphene with artificially-enhanced spin-orbit coupling
• Unidirectional magneto-transport of linearly dispersing topological edge states
• Spin injection from topological insulator tunnel-coupled to metallic leads
• Confinement versus interface bound states in spin-orbit coupled nanowires
• Topological insulators and geometry of vector bundles
• Subband structure of a cylindrical HgTe nanowire: transition from normal type to inverted type
• Parity-protected superconducting qubit based on topological insulators
• Hard wall edge confinement in 2D topological insulators and the energy of the Dirac Point
• Tunable Topological Phase Transitions in a Piezoelectric Janus Monolayer
• Electron-electron interactions in partially mixed helical states
• Unraveling the dynamics of magnetization in topological insulator-ferromagnet heterostructures via spin-orbit torque
• Quantum-anomalous-Hall current patterns and interference in thin slabs of chiral topological superconductors
• Artificial oxide heterostructures with non-trivial topology
• Universal properties of boundary and interface charges in continuum models of one-dimensional insulators
• The topological system with a twisting edge band: position-dependent Hall resistance
• Anomalous conductance steps in three-dimensional topological insulator HgTe-based quantum point contacts
• Majorana Flat Bands in the Vortex Line of Superconducting Weyl Semimetals
• Possible Topological Superconductivity in a Topological Crystalline Insulator (Pb${}_{1-x}$Sn${}_x$)${}_{1-y}$In${}_y$Te
• The magnetoelectric effect due to a semispherical capacitor surrounded by a spherical topologically insulating shell
• Engineering Topological Nodal Line Semimetals in Rashba Spin-Orbit Coupled Atomic Chains
• Quantum Parity Hall effect in ABA Graphene
• Detection of topological states in two-dimensional Dirac systems by the dynamic spin susceptibility
• Topological p-n junctions in helical edge states
• Theoretical investigation of the applicability of the Meservey-Tedrow technique to the surface states of topological insulators
• Dirac topological insulator in the d${}_{z^2}$ manifold of a honeycomb oxide
• Quantized Spin Hall Effect in Three-Dimensional Nodal-Ring Semimetal: Geometric Scaling and Symmetry-Engineered Spin Response
• Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry
• Band inversion transition in HgTe nanowire grown along the [001] direction
• Kondo effect in a two-dimensional electron gas in the Persistent Spin Helix regime
• Many-particle hybridization of optical transitions from zero-mode Landau levels in HgTe quantum wells
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure
• Bulk-edge coulping induced by a moving impurity
• Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Edge Reconstruction in a Quantum Spin Hall Insulator
• Super-resonant transport of topological surface states subjected to in-plane magnetic fields
• Exact sequence between real and complex bivariant K theories and application to the Z2 pairing
• Higher-order topological insulator in cubic semiconductor quantum wells
• Protected helical transport in magnetically doped quantum wires: Beyond the one-dimensional paradigm