Low temperature thermal transport at the interface of a topological insulator and a d-wave superconductor

Abstract

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, $\hat{I}¼$, is tuned from above the impurity scattering rate ($|\hat{I}¼|\gg \hat{I}{“}_0$) to below ($|\hat{I}¼|\ll \hat{I}{“}_0$). We calculate, via Kubo formula, the universal limit ($T\to 0$) thermal conductivity, $\hat{I}{º}_0$, as a function of $\hat{I}¼$, as it is tuned through this transition. In the large and small $|\hat{I}¼|$ limits, we obtain disorder-independent, closed-form expressions for $\hat{I}{º}_0/T$. The large-$|\hat{I}¼|$ 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 $|\hat{I}¼|$ illustrate the nature of the transition between these limits, which is shown to depend on disorder in a well-defined manner.

12 pages, 5 figures