Nonequilibrium Electrical, Thermal and Spin Transport in Open Quantum Systems of Topological Superconductors, Semiconductors and Metals

We study nonequilibrium transport in various open quantum systems whose and leads/baths are made of topological superconductors (TSs), semiconductors, metals. Using Langevin equations Green’s function method, we derive exact expressions for steady-state electrical, thermal, spin current at the junctions between a system leads. validate these by comparing them with results from direct time-evolution simulations. then show how an electrical injected TS wires divides into two parts carried single electronic excitations Cooper pairs. further ballistic thermal wire phase under temperature or voltage bias. The values grow significantly near transition, where conductance displays sharp quantized peak as predicted earlier. relate to zero-frequency thermoelectric transmission coefficient wire. also observe large transition wires. introduce differential which zero-bias zero spinful phase. role superconducting baths is demonstrated thoroughly examining features zero-temperature baths. Our new findings two-terminal geometries beneficial present challenges probing emergence Majorana quasi-particles experiments.