Abstract
We discuss an extension of our earlier work on the time-dependent Landauer- Buttiker formalism for noninteracting electronic transport. The formalism can without complication be extended to superconducting central regions since the Green's functions in the Nambu representation satisfy the same equations of motion which, in turn, leads to the same closed expression for the equal-time lesser Green's function, i.e., for the time-dependent reduced one-particle density matrix. We further write the finite-temperature frequency integrals in terms of known special functions thereby considerably speeding up the computation. Simulations in simple normal metal - superconductor - normal metal junctions are also presented.
Highlights
The process of Andreev reflection[1] (AR) occurring at the interface between a normal metal (N) and a superconductor (S) is of great importance with applications in spintronics and quantum computing
We describe the leads within the wide-band approximation (WBA), where the electronic levels of the central region are in a narrow range compared to the lead bandwidth which gives for the retarded embedding self-energy
All the levels inside the bias window act as transport channels, and transitions through the superconducting states are disrupted since the energy for the incoming electrons is high enough to break possible Cooper pairs (CP); this is referred to as normal tunneling (NT)
Summary
The process of Andreev reflection[1] (AR) occurring at the interface between a normal metal (N) and a superconductor (S) is of great importance with applications in spintronics and quantum computing. Including the transient description to the formalism by studying the nonequilibrium Green’s function approach does not complicate the final result[22,23,24,25,26,27]; the physical picture is still clear and intuitive as different features of the transport setup can be directly linked to the time-dependence[28,29,30]. Background and Nambu representation We consider a quantum transport setup similar to one studied in the previous volume of this conference series[29] In this setup, a noninteracting central region is connected between metallic leads, and the Hamiltonian takes the form. Including the pairing field in the Hamiltonian of the central region adds no extra complication to the evolution of the Green’s function[31]; the only difference, compared to the earlier work in Refs.
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