Josephson junctions based on topological insulators have recently received a lot of attention due to their potential of hosting topologically protected, gapless Andreev bound states, so called Majorana fermions. However, detecting such Majorana fermions experimentally via the measurement of a 4π-periodic Josephson current is rather challenging due to issues with quasiparticle poisoning and the presence of additional trivial modes.
Here, we propose phase-dependent heat currents through topological Josephson junctions as an alternative way to probe the existence of Majorana fermions . In particular, we demonstrate that the latter manifest themselves by a minimal thermal conductance at phase difference π. The effect is immune to quasiparticle poisoning and persists in the presence of trivial modes. We propose a simple experimental setup to verify our predictions.
Furthermore, we demonstrate that topological Josephson junctions subject to a magnetic flux form highly efficient thermal switches that offer a temperature variation of up to 40% between the on and off state . While short junctions provide a sharp switching behaviour, in long junctions the switching with magnetic flux is smooth.
 B. Sothmann and E. M. Hankiewicz, Phys. Rev. B 94, 081407(R) (2016).
 B. Sothmann, F. Giazotto and E. M. Hankiewicz, New J. Phys. 19, 023056 (2017).