Anomalous Hall Effect in Symmetry Protected Toplogical Metals

Anomalous Hall effect is known to have several major contributions, including the intrinsic contribution from the Berry phase of Bloch electrons and skew scattering from impurities. Previously we showed that there exists a class of materials dubbed as symmetry protected topological (SPT) metals. In SPT metals, the intrinsic part of the Hall conductivity shows a discontinuity over the topological phase transition. Such a discontinuity is protected by a certain symmetry, like the particle-hole symmetry.

In this work, we studied the skew scattering contribution to the thermal Hall conductivity in such a system. Our model is based on a two dimensional p+ip superconductor with a supercurrent applied in a particular direction. This system breaks time reversal symmetry which is necessary for skew scattering processes. The disorder potential is modeled by a delta potential. The scattering matrix is calculated self-consistently with the Lippman-Schwinger equation. With the help of the Boltzmann transport equation, we were able to show that skew scattering does not smear out the sharp feature from the intrinsic contribution of the thermal Hall conductivity at the topological phase transition.