Description
Historically, superconducting systems have been tackled using mean-field approximations, which presents physicists with a persistent issue: the mean-field. Often, assumptions are made about the mean-field Hamiltonian of superconducting systems; thus, for a description to be completely rigorous and physical, the mathematical consistency of the mean-field Hamiltonian must be verified. While self-consistent models have been implemented for a variety of equilibrium systems, their implementation for non-equilibrium systems experiencing a voltage bias is more limited.
Self-consistent models of conventional s-wave superconductors under a voltage bias have successfully uncovered vital transport physics, such as the critical current of superconducting states, and additional structure in the differential conductance that non-self-consistent treatments fail to capture; the extension of this rigour to unconventional systems has proven challenging. Historically, transport in systems with non-local, nearest-neighbour pairing interactions has been restricted almost exclusively to non-self-consistent approximations; such descriptions are unphysical, both due to the lack of mathematical self-consistency and because they violate local charge conservation.
In this work, a framework for obtaining self-consistent solutions of superconductors under a voltage bias was outlined. The tight-binding Bogoliubov-de Gennes formalism is adopted, employing a computationally efficient recursive scheme to obtain fully self-consistent solutions for both s-wave and d-wave superconducting systems. Transport properties are interrogated by attaching a central superconducting region to a pair of semi-infinite leads, each coupled to a reservoir at infinity; a net current is induced by introducing a chemical potential imbalance between the two reservoirs.
With this framework, the non-equilibrium transport properties of superconducting systems are explored. Namely, current-voltage relations, differential conductance, and the spatial profile of the superconducting order parameter. In addition, the critical current of the superconducting state is characterised, precisely defining the point at which the system ceases to exhibit superconductivity.
| I am the presenting author | Yes |
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