Thermoelectric transport in helical edge states via chiral hydrodynamics

We study thermoelectric transport in a 1D helical liquid, as appears at the edge of a 2D topological insulator. We employ semiclassical “chiral hydrodynamics”, which directly incorporates the axial anomaly, and we consider the combination of Rashba-mediated umklapp backscattering and quenched disorder. The conductivity is computed from the balance between umklapp scattering and the anomaly; the results agree with previous bosonization calculations. We also compute the thermoelectric power (TEP) and thermal conductivity. In the clean limit, chiral hydrodynamics gives a TEP equal to the thermodynamic entropy per charge, while the Wiedemann-Franz law is violated for the thermal conductivity by umklapp scattering. In the dirty limit, the electric and thermal conductivities scale the same way with temperature, while the TEP vanishes. We will also discuss results in the nonlinear response regime.