Theory of Tunneling Processes in Quantum Structures

Abstract

A theoretical framework to build a concrete analysis method for tunneling processes through quantum structures (QSs) is proposed based on Keldysh Green's function. As a result of three steps of transformations, we deduce the general expression for the current flowing through QSs which corresponds to the nonequilibrium and the nonlinear version of the Kubo formula. It is revealed how we can achieve the general formula successfully. It is shown that, in tunneling processes through QSs, both the elastic scattering and the inelastic scattering play an essential role. Our framework is expected to be applicable to various QSs fabricated by metals, semiconductors, superconductors and magnetic materials, since our procedure is not sensitive to details of the Hamiltonian.