Phase dependence of thermal transport in graphene Josephson junctions

We study theoretically the phase-dependent thermal transport in graphene-based Josephson junctions and highlight the role of Klein-like tunneling in the thermal energy transmission. We compute the thermal conductance for both short and long junctions by solving the Dirac-Bogoliubov--de Gennes equation. Numerical results show that the thermal conductance contains distinctive signatures of the existence of Andreev bound states, enabling us to identify different superconducting pairing symmetries in graphene, including $s$-, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-, ${d}_{xy}$-, ${p}_{x}$-, and ${p}_{y}$-wave symmetries. Importantly, our results may pave the way for applications of graphene in the field of Josephson heat interferometers.