Nonlocal thermoelectric engines in hybrid topological Josephson junctions

Abstract

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 μV/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.

Thermoelectric response of Josephson junction: from ballistic to disordered

“…Thermal response of quantum hall edge has already being studies in experiment [44] and hence an similar experimental set-up involving the spin Hall edge may not be far in the future. Recent theoretical studies have explored the possibility of inducing thermoelectric effect in helical edge state-based Josephson junction involving either an anisotropic ferromagnetic barrier [45,46] or a threeterminal geometry [47][48][49]. In this work we show that thermoelectric effect can exist in the HES of QSH even in a simplest case of two terminal ballistic JJ owing to breaking of the ω → −ω symmetry of the quasi-particle transmission probabilities across the junction at finite length.…”

Quantum thermodynamic devices: from theoretical proposals to experimental reality

“…The actual phase diagrams depend sensitively on whether or not the phase parity is enforced, and thus the device could actually be used as a diagnostics tool for the presence of 4πperiodicity in Josephson junctions. Indeed, the proposal by Scharf et al 370 has already attracted follow up work in the design of engines 372,373 , and in quantum metrology and sensing [374][375][376] .…”

Non-Markovian dynamical heat engines

“…Introduction.-The trend toward miniaturization is pushing heat engines up to the level where the working medium is a small system, which requires quantum mechanics for an accurate description [1][2][3][4][5][6][7][8][9][10][11][12]. This opened several fundamental and applicative issues in the growing field of quantum thermodynamics [13][14][15][16][17][18][19][20][21][22][23][24][25][26] in the last years.…”

“…It is now easy to conclude that it is never possible to get a heat engine in the case of Markovian dynamics of the environment connected to the system via a modulated coupling. Indeed, a memoryless bath is described by a fluctuating force correlator L 1 (t) ∝ δ(t), that corresponds to a constant L1 (ω), hence inequality (11) is never satisfied, for any value of ω. Therefore, non-Markovianity is a necessary condition to achieve a working heat engine.…”