# Nonlinear transport theory in the metal with tunnel barrier

## TL;DR

This paper develops a nonlinear transport theory for electrons in metals with tunnel barriers using scattering matrix formalism, providing a simplified way to calculate nonlinear conductivity contributions in hybrid structures.

## Contribution

It introduces a general expression for mean electrical current that simplifies nonlinear conductivity calculations in metal-tunnel barrier systems.

## Key findings

- Linear approximation matches other theories.
- Ballistic transport occurs at effective barrier transmission of 1/3.
- Landauer conductivity equals 2e^2/h at this transmission.

## Abstract

Within the framework of the scattering matrix formalism the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission $\tilde T = 1/3$ the ballistic transport is realized with a value of the Landauer conductivity equal to $G = \frac{{2e^2 }}{h}$.