Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems

TL;DR

This paper introduces a theoretical framework for magnetic noise spectroscopy in 2D materials, enabling the probing of local electronic correlations and transport regimes, including hydrodynamic behavior and impurity effects.

Contribution

It develops a comprehensive theory linking magnetic noise measurements to electronic transport properties and impurity signatures in 2D systems, with practical experimental proposals.

Findings

Hydrodynamic transport exhibits a distinct magnetic noise signature.

Magnetic noise can quantify electronic viscosity in 2D materials.

Impurity effects are detectable via noise suppression related to scattering cross-section.

Abstract

We develop the theoretical framework for calculating magnetic noise from conducting two-dimensional (2D) materials. We describe how local measurements of this noise can directly probe the wave-vector dependent transport properties of the material over a broad range of length scales, thus providing new insight into a range of correlated phenomena in 2D electronic systems. As an example, we demonstrate how transport in the hydrodynamic regime in an electronic system exhibits a unique signature in the magnetic noise profile that distinguishes it from diffusive and ballistic transport and how this can be used to measure the viscosity of the electronic fluid. We employ a Boltzmann approach in a two-time relaxation-time approximation to compute the conductivity of graphene and quantitatively illustrate these transport regimes and the experimental feasibility of observing them. Next, we discuss signatures of isolated impurities lodged inside the conducting 2D material. The noise near an impurity is found to be suppressed compared to the background by an amount that is directly proportional to the cross-section of electrons/holes scattering off of the impurity. We use these results to outline an experimental proposal to measure the temperature dependent level-shift and line-width of the resonance associated with an Anderson impurity.