Quantum transport theory of hybrid superconducting systems

We present a quantum transport theory for hybrid superconducting systems based on our exact master-equation approach. The system-terminal transport current dynamics are fully captured by the extended nonequilibrium Green's function incorporating pair correlations via spectral density matrices. The total transient transport current is decomposed into components that describe coherent transports through different paths of particle and hole channels. We show that these coherent transports are resultant interferences of numerous repeated tunneling processes and cannot be rendered as a simple normal transmission or Andreev reflection as usually described in the steady quantum transport involving superconductivity. As a practical application, we apply the theory to a two-terminal superconductor-semiconductor nanowire to study the transport dynamics through a pair of Majorana zero modes. We find that the coherent transport currents passing through a pair of well-separated Majorana zero modes vanish due to the totally destructive interference between the particle and hole channels. This provides a different understanding to the scenario of "teleportation"via a pair of delocalized Majorana zero modes, namely, a pair of delocalized Majorana zero modes does not possess the nonlocality of an entangled pair for quantum teleportation.