Low-Temperature Thermal Transport at the Interface of a Topological Insulator and a d-Wave Superconductor

We consider the low-temperature thermal transport properties of the 2D proximity-induced superconducting state formed at the interface between a topological insulator (TI) and a d-wave superconductor (dSC). This system is a playground for studying massless Dirac fermions, as they enter both as quasiparticles of the dSC and as surface states of the TI. For TI surface states with a single Dirac point, the four nodes in the interface-state quasiparticle excitation spectrum coalesce into a single node as the chemical potential, $\mu$, is tuned from above the impurity scattering rate ($|\mu| \gg \Gamma_{0}$) to below ($|\mu| \ll \Gamma_{0}$). We calculate, via Kubo formula, the universal limit ($T \rightarrow 0$) thermal conductivity, $\kappa_{0}$, as a function of $\mu$, as it is tuned through this transition. In the large and small $\mu$ limits, we obtain disorder-independent, closed-form expressions for $\kappa_{0}/T$. The large-$\mu$ expression is exactly half the value expected for a dSC, a demonstration of the sense in which the TI surface topological metal is half of an ordinary 2D electron gas. Our numerical results for intermediate $\mu$ illustrate the nature of the transition between these limits, which is shown to depend on disorder in a well-defined manner.