A quantum bound on the 1/f noise in semiconductors with a conical energy-momentum dispersion

TL;DR

This paper derives a fundamental quantum lower bound on 1/f noise in semiconductors with conical dispersion, explaining its properties and matching experimental observations, especially in graphene.

Contribution

It provides the first explicit quantum bound on 1/f noise for materials with conical dispersion, linking quantum indeterminacy to observable noise characteristics.

Findings

The quantum bound exhibits 1/f noise characteristics.

A sharp peak in noise magnitude occurs at low charge carrier density.

The model's predictions align closely with experimental data in graphene.

Abstract

The quantum indeterminacy caused by non-commutativity of observables at different times sets a lower bound on the voltage noise power spectrum in any conducting material. This bound is calculated explicitly in the case of semiconductors with a conical energy-momentum dispersion of charge carriers. It possesses all characteristic properties of 1/f noise. Its momentum decomposition is found to be singular at zero particle momentum, a measurable consequence being a sharp peak in the noise magnitude at small charge carrier density. In application to monolayer graphene, this peak becomes M-shaped on account of a continuous transition from the electron to hole conductivity. A comparison with experimental data is made which demonstrates that the calculated power spectrum is close in magnitude and congruent to the observed.