Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

Abstract

We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an "inverted" type at a critical thickness $d_c$. We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.

22 pages. Submitted to Science for publication on Aug 14, 2006

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• Dissipationless Quantum Spin Current at Room Temperature
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators

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• Surface plasmon polaritons in topological insulator
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• Transport in a Single Self-Doped Nanocrystal
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• Current noise from a magnetic moment in a helical edge
• Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of Rényi-Wehrl entropy
• Electronic properties of SnTe-class topological crystalline insulator materials
• The evolution of magnetic structure driven by a synthetic spin-orbit coupling in two-component Bose-Hubbard model
• Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity
• Robustness of the helical edge states in topological insulators
• Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian
• Optimizing the Majorana character of SQUIDs with topologically non-trivial barriers
• Disordered Chern insulator with a two step Floquet drive
• Exact solutions for a type of electron pairing model with spin-orbit interactions and Zeeman coupling
• Two distinct topological phases in the mixed valence compound YbB6 and its differences from SmB6
• Cellular dynamical mean-field theory study of an interacting topological honeycomb lattice model at finite temperature
• Kondo effect in a quantum wire with spin-orbit coupling
• Strain-tunable topological quantum phase transition in buckled honeycomb lattices
• Interaction driven quantum phase transition in fractional quantum spin Hall effects
• Quantum spin Hall insulators in centrosymmetric thin films composed from topologically trivial BiTeI trilayers
• Triple point semimetal and topological phase transitions in NaCu${}_3$Te${}_2$
• Spin-orbit coupled Bose-Einstein condensates in a double well
• Spin-orbit spillage as a measure of band inversion in insulators
• Transport in two-dimensional disordered semimetals
• Transverse angular momentum in topological photonic crystals
• Hidden edge Dirac point and robust quantum edge transport in InAs/GaSb quantum wells
• Size Effects on Transport Properties in Topological Anderson Insulators
• Landau levels, self-adjoint extensions and Hall conductivity on a cone
• Intrinsic Spin Hall Effect in s-wave Superconducting State: Analysis of Rashba Model
• Robustness of Topological Superconductivity in Proximity-Coupled Topological Insulator Nanoribbons
• Gate voltage controlled electronic transport through a ferromagnet/normal/ferromagnet junction on the surface of a topological insulator
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• Coulomb drag between helical edge states
• The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields
• Non-Equilibrium Transport Through a Gate-Controlled Barrier on the Quantum Spin Hall Edge
• Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions
• Topological semimetal-to-insulator phase transition between noncollinear and noncoplanar multiple-Q states on a square-to-triangular lattice
• Entanglement Chern number for an extensive partition of a topological ground state
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Dynamics of tunneling into nonequilibrium edge states
• Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
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• Band inversion at critical magnetic fields in a silicene quantum dot
• A Strongly-Interacting Dirac Liquid on the Surface of a Topological Kondo Insulator
• Time-reversal-invariant topological superconductivity in n-doped BiH
• Helical edge states in multiple topological mass domains
• Two-dimensional electron gas in monolayer InN quantum wells
• Prediction of topological insulating behavior in Hg2CuTi-type Heusler compounds from first principles
• Helical bound states in the continuum of the edge states in two dimensional topological insulators
• Two-Dimensional Large Gap Topological Insulators with Large Rashba Spin-Orbit Coupling in Group-IV films
• A tight-binding investigation of biaxial strain induced topological phase transition in GeCH${}_3$
• Generalized Slater-Pauling rule for the inverse Heusler compounds
• Quantum Hall effect in n-p-n and n-2D Topological Insulator-n junctions
• In-gap impurity states as the hallmark of the Quantum Spin Hall phase
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
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• Entanglement Spectrum and Entanglement Hamiltonian of a Chern insulator with open boundaries
• Characterizing the weak topological properties: Berry phase point of view
• Giant mesoscopic spin Hall effect on surface of topological insulator
• Aharonov Bohm effect in 2D topological insulator
• Unified Topological Response Theory for Gapped and Gapless Free Fermions
• Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells
• Engineered Near-Perfect Back-Scattering on Surface of Topological Insulator with Non-Magnetic Impurities
• Electronic states induced by nonmagnetic defects in two-dimensional topological insulators
• Effects of Defects and Dephasing on Charge and Spin Currents in Two-Dimensional Topological Insulators
• Backscattering in a helical liquid induced by Rashba spin-orbit coupling and electron interactions: locality, symmetry, and cutoff aspects
• ARPES study of the epitaxially grown topological crystalline insulator SnTe(111)
• Quantum spin Hall effect in rutile-based oxide multilayers
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• Ballistic transport through irradiated graphene
• Spin- and angle-resolved photoemission on the topological Kondo Insulator candidate: SmB6
• Topological phase in a two-dimensional metallic heavy-fermion system
• Search for localized Wannier functions of topological band structures via compressed sensing
• Topological transport in a spin-orbit coupled bosonic Mott insulator
• Finite frequency noise in a quantum point contact between helical edge states
• Percolating States in the Topological Anderson Insulator
• Topological phase transition and quantum spin Hall state in TlBiS${}_2$
• Entropic uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials
• Chiral topological excitons in the monolayer transition metal dichalcogenides
• Influence of etching processes on electronic transport in mesoscopic InAs/GaSb quantum well devices
• Spin-current diode with a ferromagnetic semiconductor
• Topological states in normal and superconducting $p$-wave chains
• Three-Dimensional Fractional Topological Insulators in Coupled Rashba Layers
• Rashba coupling and magnetic order in correlated helical liquids
• Band Structure of Two-dimensional Dirac Semimetal from Cyclotron Resonance
• Large Chern Number Topological Superfluids in Coupled Layer System
• Properties of A Class of Topological Phase Transition
• Dynamical competition between Quantum Hall and Quantum Spin Hall effects
• 2D and 3D topological phases in BiTe$X$ compounds
• Dimensional evolution between one- and two-dimensional topological phases
• Self-consistent study of Abelian and non-Abelian order in a two-dimensional topological superconductor
• Fabrication and characterization of the gapless half-Heusler YPtSb thin films
• Finite Size Effect in the Quantum Anomalous Hall system
• Stability and accuracy control of $\mathbf{k}\cdot \mathbf{p}$ parameters
• Spin Texture and Mirror Chern number in Hg-Based Chalcogenides
• Fractional Spin Hall Effect in Atomic Bose Gases
• Topological transport in Dirac electronic systems: A concise review
• Dirac cone in iron-based high Tc superconductors
• Josephson effect in normal and ferromagnetic topological insulator planar, step and edge junctions
• Planar tunneling spectroscopy of the topological Kondo insulator SmB${}_6$
• Gauge theory of topological phases of matter
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice
• Topological flat bands in optical checkerboard-like lattices
• Topological Floquet states on a Möbius band irradiated by circularly polarised light
• Searching for two-dimensional Weyl superconductors in heterostructures
• Interplay between Rashba interaction and electromagnetic field in the edge states of a 2D topological insulator
• Survival of sharp $n=0$ Landau levels in massive tilted Dirac fermions: Protection by generalized chiral operator
• Probing the Band Topology of Mercury Telluride through Weak Localization and Antilocalization
• Various probes of Dirac matter: from graphene to topological insulators
• Edge stability and edge quantum criticality in 2D interacting topological insulators
• An edge index for the Quantum Spin-Hall effect
• Field-angle-dependent low-energy excitations around a vortex in the superconducting topological insulator CuxBi2Se3
• Coherent Single Spin Source based on topological insulator
• Transport signatures in topological systems coupled to AC fields
• Time-reversal Invariant SU(2) Hofstadter Problem in Three Dimensional Lattices
• Lattice-matched heterojunctions between topological and normal insulators: A first-principles study
• One-dimensional Dirac electrons on the surface of weak topological insulators
• Structural versus electronic distortions of symmetry-broken IrTe${}_2$
• Screening properties and plasmons of Hg(Cd)Te quantum wells
• Quantum transport in topological insulator hybrid structures -- A combination of topological insulator and superconductor
• Topological quantum phase transition and the Berry phase near the Fermi surface in hole-doped quantum wells
• Diffusive-Ballistic Crossover and the Persistent Spin Helix
• A new kind of 2D topological insulators BiCN with a giant gap and its substrate effects
• Thermal conductivity of local moment models with strong spin-orbit coupling
• Coupled two-component atomic gas in an optical lattice
• Self-consistent $\text{k}\cdot \text{p}$ calculations for gated thin layers of 3D Topological Insulators
• Emergence of Dirac-like bands in the monolayer limit of epitaxial Ge films on Au(111)
• Topological phase in non-centrosymmetric material NaSnBi
• Edge states in the three-quarter filled system, $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models
• Vortices and vortex states in Rashba spin-orbit-coupled condensates
• Non-magnetic defects in the bulk of two-dimensional topological insulators
• Disentangled topological numbers by a purification of entangled mixed states for non-interacting fermion systems
• Effects of disorder on electron tunneling through helical edge states
• Straining the Identity of Majorana Fermions
• Topological phase transitions in bulk
• Electric control of the bandgap in quantum wells with band-inverted junctions
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• Disordered topological metals
• A 50/50 electronic beam splitter in graphene nanoribbons as a building block for electron optics
• Gapless interface states at the junction between two topological insulators
• Interaction effects in non-equilibrium transport properties of a four-terminal topological corner junction
• Nonlocal Andreev reflection, fractional charge and current-phase relation in topological bilayer exciton condensate junctions
• Single-Dirac-cone Z2 topological insulator phases in distorted Li2AgSb-class and related quantum critical Li-based spin-orbit compounds
• Classical spins in topological insulators
• Tunable spin-polarized edge transport in inverted quantum-well junctions
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• Emergence of superconductivity in a doped single-valley quadratic band crossing system of spin-1/2 fermions
• Topological quantization of ensemble averages
• Spin-triplet $f$-wave symmetry in superconducting monolayer $Mo{S}_2$
• Edge absorption and pure spin current in 2D topological insulator in the Volkov-Pankratov model
• Topological bands in one-dimensional periodic potentials
• Effect of surface hybridization on RKKY coupling in ferromagnet/topological insulator/ferromagnet trilayer system
• Non-magnetic Stern-Gerlach Experiment from Electron Diffraction
• Chern insulating state in laterally patterned semiconductor heterostructures
• Ginzburg-Landau-type theory of non-polarized spin superconductivity
• Plasmon modes in the magnetically doped Single Layer and Multilayers of Helical Metals
• Topological spinon bands and vison excitations in spin-orbit coupled quantum spin liquids
• Quantized electromagnetic response of three-dimensional chiral topological insulators
• Dynamical response of dissipative helical edge states
• Weak Electron-Phonon Coupling and Unusual Electron Scattering of Topological Surface States in Sb(111) by Laser-Based Angle-Resolved Photoemission Spectroscopy
• Electrical modulation of the edge channel transport in topological insulators coupled to ferromagnetic leads
• Zeeman field induced non-trivial topology in a spin-orbit coupled superconductor
• Novel Majorana mode and magnetoresistance in ferromagnetic superconducting topological insulator
• Current enhancement through a time dependent constriction in fractional topological insulators
• Weak localization in mesoscopic hole transport: Berry phases and classical correlations
• Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons
• Fractionalized Metals and Superconductors in Three Dimensions
• Quantum spin Hall effect in a two-orbital model on a honeycomb lattice
• Nonlocal transport in a hybrid two-dimensional topological insulator
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Measuring the Chern number with quantum oscillations
• Charge conservation protected topological phases
• Exactly solvable model of topological insulator realized on spin-1/2 lattice
• Weyl states and Fermi arcs in parabolic bands
• An envelope function formalism for lattice-matched heterostructures
• Dynamical probing of a topological phase of bosons in one dimension
• Quantum interference in HgTe structures
• A topological Dirac insulator in a quantum spin Hall phase (experimental realization of a 3D Topological Insulator)
• Unveiling a crystalline topological insulator in a Weyl semimetal with time-reversal symmetry
• Interacting topological phases in thin films of topological mirror Kondo insulators
• Buried topological edge state associated with interface between topological band insulator and Mott insulator
• Exotic Topological States with Raman-Induced Spin-Orbit Coupling
• Short-ranged interaction effects on $Z_2$ topological phase transitions
• Transmission in graphene-topological insulator heterostructures
• Effect of chiral selective tunneling on quantum transport in magnetic topological-insulator thin films
• Phonons and elasticity in critically coordinated lattices
• Four-Step Evolution of Spin-Hall Conductance: Tight-Binding Electrons with Rashba Coupling in a Magnetic Field
• Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator
• Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade
• Optical transitions in two-dimensional topological insulators with point defects
• Unwinding of a one-dimensional topological superconductor
• Optical effects of spin currents in semiconductors
• Photoabsorption spectra and the X-ray edge problem in graphene
• The effects of dissipation on topological mechanical systems
• Competing interactions in population-imbalanced two-component Bose-Einstein condensates
• Dissociation of Feshbach molecules via spin-orbit coupling in ultracold Fermi gases
• Index of Dirac operators and classification of topological insulators
• Exact solution for many-body Hamiltonian of interacting particles with linear spectrum
• Probing surface states exposed by crystal terminations at arbitrary orientations of three-dimensional topological insulators
• Sorting and Routing Topologically Protected Edge States by their Valleys
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Dynamics of Anderson localization in disordered wires
• Topological Crystalline Metal in Orthorhombic Perovskite Iridates
• Tuning the Chern number and Berry curvature with spin-orbit coupling and magnetic textures
• Topological quantum phase transition in strongly correlated Kondo insulators in 1D
• Electronic states, pseudo-spin, and transport in the zinc-blende quantum wells and wires with vanishing band gap
• A toy model for quantum spin Hall effect
• Spin-orbit density wave: A new phase of matter applicable to the hidden order state of URu2Si2
• Ultra-high mechanical stretchability and controllable topological phase transitions in two-dimensional arsenic
• Tunneling between helical Majorana modes and helical Luttinger liquids
• From The Quantum Hall Effect To Topological Insulators
• Engineering Dirac electrons emergent on the surface of a topological insulator
• Solitons and spin transport in graphene boundary
• Stability of the X-Y-phase of the two-dimensional C4 point group insulator
• Excitonic gap generation in thin-film topological insulators
• Emergent topological mirror insulator in t2g-orbital systems
• Non-necessity of band inversion process in 2D topological insulators for bulk gapless states and topological phase transitions
• Surface states around a vortex in topological superconductors: Intersection of a surface and a vortex
• Long-range Coulomb interaction effects on the surface Dirac electron system of a three-dimensional topological insulator
• Current Modulator based on Topological Insulator with Sliding Magnetic Superlattice
• Pumping conductance, the intrinsic anomalous Hall effect, and statistics of topological invariants
• Valence Bond Phases in $S=1/2$ Kane-Mele-Heisenberg Model
• Unconventional quantized edge transport in the presence of inter-edge coupling in intercalated graphene
• Valley Spin Sum Rule for Dirac Fermions: Topological Argument
• Short-ranged interaction effects on $Z_2$ topological phase transitions: The perturbative mean-field method
• Tuning the vertical location of helical surface states in topological insulator heterostructures via dual-proximity effects
• Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene
• Controlling scattering of light through topological transitions in all-dielectric metasurfaces
• Spin and electric currents induced by a spin-motive force in two-dimensional Dirac semimetals protected by nonsymmorphic symmetries
• First Principles Prediction of Topological Phases in Thin Films of Pyrochlore Iridates
• Photonic analogue of quantum spin Hall effect
• Topological Weyl-like Phonons and Nodal Line Phonons in Graphene
• Superfluid Transition in a Chiron Gas
• Large Enhancement of Electronic Thermal Conductivity and Lorenz Number in Topological Insulator Bi2Te2Se Thin Films
• Two dimensional photonic quasicrystal edge states protected by second Chern number
• Splitting of the topologically-protected Dirac cone without breaking time reversal symmetry
• Low-Frequency Current Fluctuations in Graphene-like Exfoliated Thin-Films of Topological Insulators
• A Spinning Particle in a Mobius Strip