Spontaneous thermal Hall conductance in superconductors with broken time-reversal symmetry

Abstract

The thermal Hall conductivities (THCs) κij have extensively been studied in recent condensed matter experiments. THCs can spontaneously become nonzero for a time-reversal-symmetry-broken system, and have a contribution from topologically protected edge states. Here, we focus on an additional bulk effect, the impurity mechanism in superconductors (SCs). Previously, the THCs were calculated for the chiral p-wave [S. K. Yip, Supercond. Sci. Technol. 29, 085006 (2016)10.1088/0953-2048/29/8/085006; B. Arfi et al., Phys. Rev. B 39, 8959 (1989)10.1103/PhysRevB.39.8959] SCs for point impurities. Generalizing this finding to even-pairing states, we calculate thermal transport coefficients for finite-size impurities using Keldysh quasiclassical Green's functions. We find that for d-wave pairing, the impurity mechanism is dominant in κyx when compared to the topological contribution except at very low temperatures. This finding is shown to be valid irrespective of the impurity density of the bulk. There are two experimental signatures of the impurity mechanism on κyx: a nonmonotonic temperature dependence and a possible sign change as a function of temperature depending on the scattering phase shifts and the corresponding d-wave representation.