Direct calculation of the tunneling current

TLDR

The model uses localized functions to avoid the difficult matching problem at the barrier‑electrode boundary in tunneling junctions. The study proposes a simple Hamiltonian for a metal‑insulator‑metal junction that enables direct calculation of the tunneling current and can be extended to include many‑body effects. The authors employ a localized‑function Hamiltonian together with Kjeldysh perturbation theory to compute the current to all orders in bias without introducing an effective Hamiltonian. The transfer coefficient appearing in the current expression is energy dependent.

Abstract

A simple model Hamiltonian is proposed for a metal-insulator- metal tunneling junction, which permits the direct calculation of the tunneling current without introducing any effective Hamiltonian. The model rests on the use of localized functions; this procedure avoids the difficult matching problem at the boundary between the barrier and the electrodes. Moreover the use of Kjeldysh's perturbation theory for nonequilibrium system allows an explicit calculation of the current to all orders in the applied bias. It is found that the transfer coefficient appearing in the expression for the current is energy dependent. This model can be systematically extended to include many body effects.