The Helical Liquid and the Edge of Quantum Spin Hall Systems

Abstract

The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the ``helical liquid'', where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal (TR) symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the TR invariance. The Kondo effect in such a liquid exhibits new features in the structure of the screening cloud.

4 pages, accepted by Phys. Rev. Lett

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• Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
• Noncentrosymmetric superconductors in one dimension
• Band manipulation and spin texture in interacting moiré helical edges
• Plasmons in single- and double-component helical liquids: Application to two-dimensional topological insulators
• Detection of entanglement by helical Luttinger liquids
• Spin current in an electron waveguide tunnel-coupled to topological insulator
• Tunneling between a topological superconductor and a Luttinger liquid
• Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures
• Sub- to Super-Poissonian crossover of current noise in helical edge states coupled to a spin impurity in a magnetic field
• Buried topological edge state associated with interface between topological band insulator and Mott insulator
• Mirror anomaly in fermionic topological orders
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Quantum spin Hall phase in neutral zigzag graphene ribbons
• A-geometrical approach to Topological Insulators with defects
• Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations
• Fractionalized Spin Excitations in the Edge Ferromagnetic State of Graphene: Signature of the Ferromagnetic Luttinger Liquid
• Two-channel Kondo problem in coupled interacting helical liquids
• Chiral detection of Majorana bound states at the edge of a quantum spin Hall insulator
• Electron transport in a ferromagnetic/normal/ferromagnetic tunnel junction based on the surface of a topological insulator
• Electrically tunable two-channel Kondo fixed points in helical liquids
• Double Dirac cones in band structures of periodic Schrödinger operators
• Topology of Discrete Quantum Feedback Control
• Tailoring topological states in silicene using different halogen-passivated Si(111) substrates
• Asymmetric Cherenkov acoustic reverse in topological insulators
• Topological and magnetic properties of the interacting Bernevig-Hughes-Zhang model
• Backscattering off a driven Rashba impurity at the helical edge
• Boundary and defect criticality in topological insulators and superconductors
• Transport in quantum spin Hall edges in contact to a quantum dot
• Quantum criticality in Kondo quantum dot coupled to helical edge states of interacting 2D topological insulators
• Quantum phase diagram of Shiba impurities from bosonization
• Helical superconducting edge modes from pseudo-Landau levels in graphene
• Marginally localized edges of time-reversal symmetric topological superconductors
• Electronic thermal conductivity in 2D topological insulator in a HgTe quantum well
• Transport in Magnetically Doped One-Dimensional Wires: Can the Helical Protection Emerge without the Global Helicity?
• 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
• Correlation and current anomalies in helical quantum dots
• Quantum spin Hall insulator in proximity with a superconductor: Transition to the Fulde-Ferrell-Larkin-Ovchinnikov state driven by a Zeeman field
• Intrinsic (Axion) Statistical Topological Insulator
• Phase-tunable multiple Andreev reflections in a quantum spin Hall strip
• Interference effects induced by a precessing easy-plane magnet coupled to a helical edge state
• Spin-polarized voltage probes for helical edge state: a model study
• Tunneling spectroscopy between one-dimensional helical conductors
• Effective field theories for interacting boundaries of 3D topological crystalline insulators through bosonisation
• Time-dependent potential impurity in topological insulator
• Tunneling between helical Majorana modes and helical Luttinger liquids
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System
• Kinetic processes in Fermi-Luttinger liquids
• Exciton Condensation in Landau Levels of Quantum Spin Hall Insulators
• Charge and spin density in the helical Luttinger liquid
• Nonequilibrium Spectroscopy of Topological Edge Liquids
• Reentrant quantum spin Hall effect in the presence of an exchange field
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• The chiral SYK model in three-dimensional holography
• Antiferromagnetic topological insulators in heavy-fermion systems
• Natural orbitals renormalization group approach to a spin-1/2 impurity interacting with two helical liquids
• The Symmetry Principle in Condensed Matter Physics (I)
• Magnetic correlation between two local spins in a quantum spin Hall insulator
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Emergent Carroll symmetry at phase separation in one-dimensional lattice systems
• Unidirectional magneto-transport of linearly dispersing topological edge states
• Cyclotron Dynamics of a Kondo Singlet in a Spin-Orbit-Coupled Alkaline-Earth Atomic Gas
• Finite-temperature spectroscopy of dirty helical Luttinger liquids
• Photocurrent and photoconductance of an helical edge state
• Electrically-detected single-spin resonance with Quantum Spin Hall edge states
• Dynamic impurities in two-dimensional topological insulator-edge states
• Electron-electron interactions in partially mixed helical states
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Quantum critical points in tunneling junction of topological superconductor and topological insulator
• Variational Tensor Wavefunctions for the Interacting Quantum Spin Hall Phase
• Unconventional quantized edge transport in the presence of inter-edge coupling in intercalated graphene
• Helical edge states induced by lateral spin-orbit coupling
• Topological p-n junctions in helical edge states
• Emergence of a new symmetry class for Bogoliubov-de Gennes (BdG) Hamiltonians: Expanding ten-fold symmetry classes
• A non-perturbative expression for the transmission through a leaky chiral edge mode
• Dissipative Hot-spot Enabled Shock and Bounce Dynamics via Terahertz Quantum Quenches in Helical Edge States
• Anomalous flux periodicity in proximitised quantum spin Hall constrictions
• Analytical theory and possible detection of the $ac$ quantum spin Hall effect
• Inter-species topological phases via a dynamical gauge field
• The topological system with a twisting edge band: position-dependent Hall resistance
• Volkov-Pankratov states on the edge of a quantum spin Hall system
• Spin responses of a disordered helical superconducting edge under Zeeman field
• Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering
• Orbital ferromagnetism in interacting few-electron dots with strong spin-orbit coupling
• To See a World in a Grain of Sand -- The Scientific Life of Shoucheng Zhang
• Hydrodynamic theory of surface excitations of three-dimensional topological insulators
• Boundary criticality in two-dimensional interacting topological insulators
• Emergent Symmetry and Phase Transitions on the Domain Wall of ${\mathbb{Z}}_2$ Topological Orders
• Orthogonal Cherenkov sound in spin-orbit coupled systems
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges
• Detection of fractional solitons in quantum spin Hall systems
• Symmetry-protected topological corner modes in a periodically driven interacting spin lattice
• Multiband quasiparticle interference in the topological insulator Cu_(x)Bi_(2)Te_(3)
• Manipulation of helical states revealed by crossed Andreev reflection
• Local Density of States in a Helical Tomonaga-Luttinger Liquid of Loop and Josephson Junction Geometries
• Surface states of gapped electron systems and semi-metals
• A Study of Asymptotic Freedom like Behavior for Topological States of Matter
• Electronic correlations in magnetized helical edge states coupled to s-wave superconductors
• Symmetry-protected topological wire in a topological vacuum