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We study nonequilibrium transport in various open quantum systems whosesystems and leads/baths are made of topological superconductors (TSs),semiconductors, and metals. Using quantum Langevin equations and Green'sfunction method, we derive exact expressions for steady-state electrical,thermal, and spin current at the junctions between a system and leads. Wevalidate these current expressions by comparing them with the results fromdirect time-evolution simulations. We then show how an electrical currentinjected in TS wires divides into two parts carried by single electronicexcitations and Cooper pairs. We further show ballistic thermal transport in anopen TS wire in the topological phase under temperature or voltage bias. Thethermal current values grow significantly near the topological phasetransition, where thermal conductance displays a sharp quantized peak aspredicted earlier. We relate the quantized thermal conductance to thezero-frequency thermoelectric transmission coefficient of the open TS wire. Wealso observe a large thermoelectric current near the topological transition ofthe TS wires. We introduce a differential spin conductance which displays aquantized zero-bias peak at zero temperature for a spinful TS wire in thetopological phase. The role of superconducting baths in transport isdemonstrated by thoroughly examining the features of zero-temperaturedifferential electrical conductance and thermal conductance in open systemswith TS baths. Our new thermoelectric and spin transport findings in varioustwo-terminal geometries are beneficial to the present challenges in probing theemergence of Majorana quasi-particles in experiments.

Nonequilibrium electrical, thermal and spin transport in open quantum systems of topological superconductors, semiconductors and metals