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

The thermal Hall conductivities(THCs), $\kappa_{ij}$s have extensively been studied in recent condensed matter experiments. THC can spontaneously become non-zero for a time-reversal symmetry (TRS) broken system, and have a contribution from topologically protected edge states. In this talk, we focus on an additional bulk effect, the impurity pair breaking mechanism(IPM) in superconductors (SCs). Previously, the THCs were calculated for the chiral p-wave[1-2] SCs for point impurities. Motivated by d-wave TRS broken SCs; URu$_2$Si$_2$, SrPtAs including Sr$_2$RuO$_4$ which is recently suggested to be also possibbly, we calculate THCs at finite temperatures and for finite size impurities using the non-equilibrium quasiclassical Green's functions.

We find that the IPM is dominant in $\kappa_{yx}$ at finite temperatures when compared to the topological contribution except at very low temperatures. There are two experimental signatures of IPM: 1. a non-monotonic temperature dependence, 2. sign change as a function of temperature depending on the scattering process.

[1] S. Yip, Sup. Sci. Technol. 29, 085006 (2016).
[2] Arfi et al., Phy. Rev. B 39, 8959 (1989)