Electronic Transport in Hybrid Mesoscopic Structures: A Nonequilibrium Green Function Approach

TL;DR

This paper develops a comprehensive theoretical framework using nonequilibrium Green functions to analyze electronic transport in hybrid mesoscopic structures involving superconductors and ferromagnets, accounting for strong correlations and nonequilibrium conditions.

Contribution

It introduces a general, gauge-invariant current formula applicable to various hybrid systems, unifying descriptions for both strongly correlated and noninteracting cases.

Findings

Derived a general current formula using Keldysh Green functions

Demonstrated the formula's dependence on relative phase and magnetization orientations

Showed the formula reduces to known models like Meir-Wingreen and Landauer-Büttiker

Abstract

We present a unified transport theory of hybrid structures, in which a confined normal state ($N$) sample is sandwiched between two leads each of which can be either a ferromagnet ($F$) or a superconductor ($S$) via tunnel barriers. By introducing a four-dimensional Nambu-spinor space, a general current formula is derived within the Keldysh nonequilibrium Green function formalism, which can be applied to various kinds of hybrid mesoscopic systems with strong correlations even in the nonequilibrium situation. Such a formula is gauge invariant. We also demonstrate analytically for some quantities, such as the difference between chemical potentials, superconductor order parameter phases and ferromagnetic magnetization orientations, that only their relative value appears explicitly in the current expression. When applied to specific structures, the formula becomes of the Meir-Wingreen-type favoring strong correlation effects, and reduces to the Landauer-B\"uttiker-type in noninteracting systems such as the double-barrier resonant structures, which we study in detail beyond the wide-band approximation.