Thermodynamics in topological Josephson junctions

Abstract

We study the thermodynamic properties of topological Josephson junctions using a quantum spin Hall (QSH) insulator-based junction as an example. In particular, we propose that phase-dependent measurements of the heat capacity offer an alternative to Josephson-current measurements to demonstrate key topological features. Even in an equilibrium situation, where the fermion parity is not conserved, the heat capacity exhibits a pronounced double peak in its phase dependence as a signature of the protected zero-energy crossing in the Andreev spectrum. This double-peak feature is robust against changes of the tunneling barrier and thus allows one to distinguish between topological and trivial junctions. At short time scales fermion parity is conserved and the heat capacity is 4π-periodic in the superconducting phase difference. We propose a dispersive setup coupling the Josephson junction to a tank LC circuit to measure the heat capacity of the QSH-based Josephson junction sufficiently fast to detect the 4π-periodicity. Although explicitly calculated for a short QSH-based Josephson junction, our results are also applicable to long as well as nanowire-based topological Josephson junctions.

Nonlocal thermoelectric engines in hybrid topological Josephson junctions

“…[72][73][74][75]. The application of thermal gradients to Josephson junctions has also suggested unique technologies [62,[76][77][78][79][80][81][82][83], showing that the peculiar properties of TJJs could also play an important role in this perspective [19,22,[84][85][86][87][88].…”

Rashba-controlled thermal valve in helical liquids

“…However, measurements in the quantum point contact geometry in ballistic channels driven by thermal gradients have also been reported 34,45,46 . The study of the transport properties characterizing helical liquids in presence of thermal gradients has recently been carried out as well, focusing mostly on non-interacting systems and on Josephsonlike configurations with superconducting leads [49][50][51][52] . In the absence of SOC, on the other hand, the violation of the Wiedemann-Franz (WF) law, as expected for a non-Fermi liquid system, has been predicted [53][54][55][56][57] and reported 58 in 1D systems.…”