Benedikt Scharf, Alessandro Braggio, Elia Stambini, Francesco Giazotto, Ewelina M. Hankiewicz

• Topological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. WeTopological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. We discuss how this engine can be implemented as a Josephson-Stirling cycle in topological superconductors, thereby illustrating the potential of the intriguing and fruitful marriage between topology and coherent thermodynamics. It is shown that the Josephson-Stirling cycle constitutes a highly versatile thermodynamic machine with different modes of operation controlled by the cycle temperatures. Finally, the thermodynamic cycle reflects the hallmark 4 pi -periodicity of topological Josephson junctions and could therefore be envisioned as a complementary approach to test topological superconductivity. Topological superconductors are expected to be a key component of quantum computing systems but reliably detecting their exotic properties is a challenge. Here, the authors propose a topological Josephson heat engine which uses thermodynamic effects to probe the 4 pi -periodic ground state of a topological superconductor.…