Supercurrent-induced Anomalous Thermal Hall Effects as a New Probe to Superconducting Pairing Anisotropy

Two-dimensional superconductors have been realized in various atomically thin films, some of which are anticipated to involve unconventional pairing mechanisms, including twisted bilayer graphene (TBG) and FeSe. Due to the low dimensionality, experimental probes of the superconductivity in these systems have been limited. In this paper we consider a Josephson junction formed by stacking two superconducting thin films, and propose an anomalous thermal hall effect induced by the Josephson supercurrent, in the absence of an external magnetic field. Interestingly, we find that this effect sharply probes the in-plane anisotropy of the superconducting gap function $Delta_k$, which may be useful in experimental investigations on two-dimensional superconductivity in systems such as TBG.