Magnetotransport on a QSHI Edge

We develop and compare theories of nonlinear magnetotransport along the edge of a Quantum Spin Hall Insulator (QSHI). Our focus is on the current response which quadratic in the applied bias voltage and odd in the external magnetic field. Previous work modeled the linear conductance via a nonineracting theory of helical edge states coupled to bulk midgap states, which adequately explained the angular magnetic field dependence.

Building on this, we obtained a mechanism for nonlinear conductance by incorporating a Hubbard interaction term on the mid-gap states. Treating such interaction in a Hartree-Fock approximation 

captures key features of the nonlinear part of the I-V characteristic. It however requires an unrealistically small interaction strength to match the data in WTe_2.

Here we propose an additional mechanism related to the nonlinearity of the edge dispersion. This mechanism stems from redistribution of charge carriers within the two helical edge branches without changing the total number of carriers on each. We show that in the presence of an external magnetic field this leads to a current quadratic in the applied bias.