Cascade Boltzmann - Langevin approach to higher-order current correlations in diffusive metal contacts

TL;DR

This paper extends the Boltzmann-Langevin approach to calculate higher-order current correlations in diffusive metals, successfully matching quantum-mechanical results for third and fourth cumulants, revealing voltage-dependent sign changes.

Contribution

It introduces a method to compute third and fourth current cumulants in diffusive metals, bridging classical and quantum descriptions of current noise.

Findings

Third cumulant matches quantum value exactly.

Fourth cumulant approaches quantum value at high voltage.

Fourth cumulant changes sign around eV ~ 20T.

Abstract

The Boltzmann - Langevin approach is extended to calculations of third and fourth cumulants of current in diffusive-metal contacts. These cumulants result from indirect correlations between current fluctuations, which may be considered as "noise of noise". The calculated third cumulant coincides exactly with its quantum-mechanical value. The fourth cumulant tends to its quantum-mechanical value $-e^3I/105$ at high voltages and to a positive value $2e^2T/3R$ at V=0 changing its sign at $eV \sim 20T$.