Nonlocal thermoelectric engines in hybrid topological Josephson junctions

The thermoelectric performance of a topological Josephson nonlocal heat engine is thoroughly investigated. The nonlocal response is obtained by using a normal metal probe coupled to only one of the proximized helical edges in the middle of the junction. In this configuration, we investigate how the flux and phase biases trigger the nonlocal thermoelectric effects under the application of a thermal difference between the superconducting terminals. Possible experimental nonidealities such as asymmetric proximized superconducting gaps are considered, showing how the nonlocal response can be affected. The interplay between Doppler shift, which tends to close gaps, and Andreev interferometry, which affects particle-hole resonant transport, are clearly identified for different operating regimes. Finally, we discuss the power and the efficiency of the topological thermoelectric engine which reaches maximum power at maximal efficiency for a well-coupled normal probe. We find quite high nonlocal Seebeck coefficients of the order of tenths of ?V/K at a few Kelvin, a signal that would also be clearly detectable against any spurious local effects even with moderate asymmetry of the gaps.