Fundamental limits to helical edge conductivity due to spin-phonon scattering

Abstract

We study the effect of electron-phonon interactions on the electrical conductance of a helical edge state of a two-dimensional topological insulator. We show that the edge deformation caused by bulk acoustic phonons modifies the spin texture of the edge state, and that the resulting spin-phonon coupling leads to inelastic backscattering which makes the transport diffusive. Using a semiclassical Boltzmann equation we compute the electrical conductivity and show that it exhibits a metallic Bloch-Grüneisen law. At temperatures on the order of the Debye temperature of the host material, spin-phonon scattering thus lowers the conductivity of the edge state drastically. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $\delta G\propto T^5$ at low temperatures. Relying only on parallel transport of the helical spin texture along the deformed edge, the coupling strength is determined by the host material's density and sound velocity. Our results impose fundamental limits for the finite-temperature conductivity of a helical edge channel.

5 pages, 3 figures

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• Conductance of quantum spin Hall edge states from first principles: the critical role of magnetic impurities and inter-edge scattering
• Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators
• Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples
• Phase diagram and phonon-induced backscattering in topological insulator nanowires
• Suppression of ballistic helical transport by isotropic dynamical magnetic impurities
• Sub- to Super-Poissonian crossover of current noise in helical edge states coupled to a spin impurity in a magnetic field
• Finite frequency noise in chiral Luttinger liquid coupled to phonons
• Interaction- and phonon-induced topological phase transitions in double helical liquids
• Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium