Thermoelectric Transport and Shock Dynamics in Helical Edge States

We study transport and shock dynamics in one-dimensional helical liquids via chiral hydrodynamics. Helical liquids can arise as edge states of 2D Z2 topological insulators, hinge states of higher-order topological phases, in graphene under strong magnetic fields, and in quantum wires with strong spin-orbit coupling. We focus on an unusual time-reversal invariant one-particle umklapp (1PU) scattering mechanism enabled by Rasha spin-orbit coupling. Transport coefficients demonstrate the crossover between ballistic and hydrodynamic behavior. Moreover, we show that shock fronts develop due to the 1PU scattering for counterpropagating charge packets induced by an intense electric pulse. The 1PU scatterings convert right-movers at the hot leading edge of a right-moving packet into left-movers and cool them down. The slope of the density at the shock front increases in time and goes to infinity at long times. The effect is enhanced by stronger 1PU interactions and the shock front can form faster for strong interactions.

Ref. Xinghai Zhang and Matthew Foster, arXiv:2009.06654.