Higher cumulants of voltage fluctuations in current-biased diffusive contacts

TL;DR

This paper calculates the third and fourth cumulants of voltage fluctuations in a current-biased diffusive contact across various temperatures and voltages, revealing their dependence on temperature and current.

Contribution

It introduces a semiclassical cascade approach to derive explicit formulas for higher voltage cumulants in diffusive contacts at arbitrary conditions.

Findings

Third cumulant: $e^2R^3I/3$ at high T, $4e^2R^3I/15$ at low T

Fourth cumulant: $2e^2R^3T/3$ at high T, $(34/105)e^3R^4I$ at low T

Provides analytical expressions for voltage cumulants in diffusive contacts

Abstract

The third and fourth cumulants of voltage in a current-biased diffusive metal contact of resistance $R$ are calculated for arbitrary temperatures and voltages using the semiclassical cascade approach. The third cumulant equals $e^2R^3I/3$ at high temperatures and $4e^2R^3I/15$ at low temperatures, whereas the fourth cumulant equals $2e^2R^3T/3$ at high temperatures and $(34/105)e^3R^4I$ at low temperatures.