Thermal noise and dephasing due to electron interactions in non-trivial geometries

TL;DR

This paper derives a microscopic theory of Johnson-Nyquist noise in complex geometries of disordered metals, linking electric potential fluctuations to diffusion processes, and applies it to analyze dephasing in multiply-connected systems.

Contribution

It provides a general relation between potential fluctuations and density fluctuations for arbitrary geometries, and applies this to study dephasing in complex metallic networks.

Findings

Potential fluctuations are proportional to the zero-frequency diffusion solution.

Explicit correlation functions are derived for ring-shaped networks.

The theory explains dephasing effects due to electronic noise in multiply-connected systems.

Abstract

We study Johnson-Nyquist noise in macroscopically inhomogeneous disordered metals and give a microscopic derivation of the correlation function of the scalar electric potentials in real space. Starting from the interacting Hamiltonian for electrons in a metal and the random phase approximation, we find a relation between the correlation function of the electric potentials and the density fluctuations which is valid for arbitrary geometry and dimensionality. We show that the potential fluctuations are proportional to the solution of the diffusion equation, taken at zero frequency. As an example, we consider networks of quasi-1D disordered wires and give an explicit expression for the correlation function in a ring attached via arms to absorbing leads. We use this result in order to develop a theory of dephasing by electronic noise in multiply-connected systems.