Unidirectional magnetotransport of linearly dispersing topological edge states

Quantum spin Hall edges are envisaged as next-generation transistors, yet they exhibit dissipationless transport only over short distances. Here, we show that in a diffusive sample, where charge puddles with odd spin cause backscattering, a magnetic field drastically increases the mean free path and drives the system into the ballistic regime with a Landauer-Buttiker conductance. A strong nonlinear nonreciprocal current emerges in the diffusive regime with opposite signs on each edge, and vanishes in the ballistic limit. We discuss its detection in state-of-the-art experiments.