Evidence for broken Galilean invariance at the quantum spin Hall edge

We study transport properties of the helical edge channels of a quantum spin Hall (QSH) insulator, in the presence of electron-electron interactions and weak, local Rashba spin-orbit coupling. The combination of the two allows for inelastic backscattering that does not break time-reversal symmetry (TRS), resulting in interaction-dependent power law corrections to the conductance. Here, we use a non-equilibrium Keldysh formalism to describe the situation of a long, one-dimensional edge channel coupled to external reservoirs, where the applied bias is the leading energy scale. By calculating explicitly the corrections to the conductance up to fourth order of the impurity strength, we analyse correlated single- and two-particle backscattering processes on a microscopic level. Interestingly, we show that the modeling of the leads together with the breaking of Galilean invariance has important consequences on the transport properties. Such breaking occurs, because the Galilean invariance of the bulk spectrum transforms into an emergent Lorentz invariance of the edge spectrum. With this broken Galilean invariance at the QSH edge, we find a contribution to single particle backscattering with a very low power scaling, while in the presence of Galilean invariance the leading contribution would be due to correlated two-particle backscattering only. This difference is further reflected in different values of the Fano factor of the shot noise, an experimentally observable quantity. The described behaviour is specific to the Rashba scatterer, and does not occur in the case of backscattering off a time-reversal breaking, magnetic impurity.