Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples

Abstract

Understanding possible mechanisms, which can lead to suppression of helical edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. Next, we illustrate the general approach by a detailed study of representative examples. One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. Another example focuses on the effects of the space-fluctuating spin-orbit interaction on the QSH edge. It reveals weakness of the protection in several cases, including, e.g., the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron-electron interactions.

The final version, which includes a brief review and original part; 16 pages, 2 figures

References in corpus (26)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Quantum Spin Hall Effect in Inverted Type II Semiconductors
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Edge Dynamics in a Quantum Spin Hall State: Effects from Rashba Spin-Orbit Interaction
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Resistance of helical edges formed in a semiconductor heterostructure
• Conductivity of a generic helical liquid
• Spatially resolved study of backscattering in the quantum spin Hall state
• Persistence of two-dimensional topological insulator state in wide HgTe quantum well
• Spontaneous breakdown of topological protection in two dimensions
• Kondo lattice on the edge of a two-dimensional topological insulator
• Linear magnetoresistance in HgTe quantum wells
• Helical Liquids in Semiconductors
• Low-Temperature Conductivity of Weakly Interacting Quantum Spin Hall Edges in Strained-Layer InAs/GaInSb
• Current noise from a magnetic moment in a helical edge
• Backscattering in a helical liquid induced by Rashba spin-orbit coupling and electron interactions: locality, symmetry, and cutoff aspects
• Chiral Spin Order in Kondo-Heisenberg systems
• Spatial structure of correlations around a quantum impurity at the edge of a two-dimensional topological insulator
• Elastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities
• Analytical and Numerical study of the out-of-equilibrium current through a helical edge coupled to a magnetic impurity
• Suppression of ballistic helical transport by isotropic dynamical magnetic impurities
• Topological phase transition in quantum spin Hall insulator in the presence of charge lattice coupling

Cited by in corpus (6)

• Effects of charge dopants in quantum spin Hall materials
• Does delta-$T$ noise probe quantum statistics?
• Quantitative theory of backscattering in topological HgTe and (Hg,Mn)Te quantum wells: acceptor states, Kondo effect, precessional dephasing, and bound magnetic polaron
• Explicit derivation of the chiral and (generic) helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation
• RKKY to Kondo crossover in Helical Edge of a Topological Insulator
• Interaction- and phonon-induced topological phase transitions in double helical liquids