Mesoscopic conductance fluctuations in graphene samples

TL;DR

This paper analytically investigates mesoscopic conductance fluctuations in graphene, revealing how different scattering mechanisms affect the variance and explaining recent numerical and experimental findings.

Contribution

It provides a theoretical framework for understanding how valley symmetry breaking influences conductance fluctuations in graphene.

Findings

Conductance variance is four times that of metals without valley symmetry breaking.

Variance reduces to twice that of metals with strong intravalley scattering.

Variance equals that of metals when strong intervalley scattering dominates.

Abstract

Mesoscopic conductance fluctuations in graphene samples at energies not very close to the Dirac point are studied analytically. We demonstrate that the conductance variance $<[\delta G]^2>$ is very sensitive to the elastic scattering breaking the valley symmetry. In the absence of such scattering (disorder potential smooth at atomic scales, trigonal warping negligible), the variance $<[\delta G]^2 > = 4 < [\delta G]^2 >_\text{metal}$ is four times greater than that in conventional metals, which is due to the two-fold valley degeneracy. In the absence of intervalley scattering, but for strong intravalley scattering and/or strong warping $<[\delta G]^2 > =2 < [\delta G]^2 >_\text{metal}$. Only in the limit of strong intervalley scattering $<[\delta G]^2 > = < [\delta G]^2 >_\text{metal}$. Our theory explains recent numerical results and can be used for comparison with existing experiments.