Anomalous Hall Effects in Chiral Superconductors

TL;DR

This paper presents theoretical predictions for anomalous thermal and electrical transport in chiral superconductors, highlighting how impurity structure and order parameter topology influence observable Hall effects.

Contribution

It introduces a detailed theoretical framework linking impurity scattering, order parameter winding number, and thermal Hall conductivity in chiral superconductors.

Findings

Thermal Hall effect depends on the winding number of the order parameter.

Transverse heat current appears for  winding number with point-like impurities.

Finite-size impurities enable thermal Hall conductivity for  or higher winding numbers.

Abstract

We report theoretical results for the electronic contribution to thermal and electrical transport for chiral superconductors belonging to even or odd-parity E$_1$ and E$_2$ representations of the tetragonal and hexagonal point groups. Chiral superconductors exhibit novel properties that depend on the topology of the order parameter and Fermi surface, and -- as we highlight -- the structure of the impurity potential. An anomalous thermal Hall effect is predicted and shown to be sensitive to the winding number, $\nu$, of the chiral order parameter via Andreev scattering that transfers angular momentum from the chiral condensate to excitations that scatter off the random potential. For heat transport in a chiral superconductor with isotropic impurity scattering, i.e., point-like impurities, a transverse heat current is obtained for $\nu=\pm 1$, but vanishes for $|\nu|>1$. This is not a universal result. For finite-size impurities with radii of order or greater than the Fermi wavelength, $R\ge\hbar/p_f$, the thermal Hall conductivity is finite for chiral order with $|\nu|\ge2$, and determined by a specific Fermi-surface average of the differential cross-section for electron-impurity scattering. Our results also provide quantitative formulae for analyzing and interpreting thermal transport measurements for superconductors predicted to exhibit broken time-reversal and mirror symmetries.