Fingerprint of topological Andreev bound states in phase-dependent heat transport

We demonstrate that phase-dependent heat currents through superconductor-topological insulator Josephson junctions provide a useful tool to probe the existence of topological Andreev bound states, even for multi-channel surface states. We predict that in the tunneling regime topological Andreev bound states lead to a minimum of the thermal conductance for a phase difference $\phi=\pi$, in clear contrast to a maximum of the thermal conductance at $\phi=\pi$ that occurs for trivial Andreev bound states in superconductor-normal metal tunnel junctions. This opens up the possibility that phase-dependent heat transport can distinguish between topologically trivial and nontrivial 4$\pi$ modes. Furthermore, we propose a superconducting quantum interference device geometry where phase-dependent heat currents can be measured using available experimental technology.