Mapping universal conductance fluctuations

TL;DR

This paper uses a cooled scanning probe microscope to map universal conductance fluctuations in graphene, revealing high sensitivity of conductance to local scatterer position and confirming quantum simulation predictions.

Contribution

It introduces a nanoscale probing method to spatially map conductance fluctuations in graphene, advancing understanding of coherent electron transport at the nanoscale.

Findings

Conductance fluctuations of order e^2/h are observed with tip displacement.

High agreement between experimental maps and quantum simulations.

Demonstrates the effectiveness of cooled SPM in probing quantum transport.

Abstract

Graphene provides a fascinating testbed for new physics and exciting opportunities for future applications based on quantum phenomena. To understand the coherent flow of electrons through a graphene device, we employ a nanoscale probe that can access the relevant length scales - the tip of a liquid-He-cooled scanning probe microscope (SPM) capacitively couples to the graphene device below, creating a movable scatterer for electron waves. At sufficiently low temperatures and small size scales, the diffusive transport of electrons through graphene becomes coherent, leading to universal conductance fluctuations (UCF). By scanning the tip over a device, we map these conductance fluctuations \textit{vs.} scatterer position. We find that the conductance is highly sensitive to the tip position, producing $\delta G \sim e^2/h$ fluctuations when the tip is displaced by a distance comparable to half the Fermi wavelength. These measurements are in good agreement with detailed quantum simulations of the imaging experiment, and demonstrate the value of a cooled SPM for probing coherent transport in graphene.