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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, $μ$, is tuned from above the impurity scattering rate ($|μ| \gg Γ_0$) to below ($|μ| \ll Γ_0$). We calculate, via Kubo formula, the universal limit ($T \rightarrow 0$) thermal conductivity, $κ_0$, as a function of $μ$, as it is tuned through this transition. In the large and small $|μ|$ limits, we obtain disorder-independent, closed-form expressions for $κ_0/T$. The large-$|μ|$ 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 $|μ|$ illustrate the nature of the transition between these limits, which is shown to depend on disorder in a well-defined manner.