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 3D strong 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 d-wave superconductor, 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.