Neutrality point of graphene with coplanar charged impurities

TL;DR

This paper investigates the effects of in-plane charged impurities on graphene's ground state and transport properties, revealing nonlinear screening, fractal puddle structures, and a logarithmic dependence of conductivity on Coulomb interaction strength.

Contribution

It introduces a theoretical framework for understanding nonlinear impurity screening and fractal puddle formation in graphene with coplanar charged impurities, providing asymptotically exact results for small interaction strength.

Findings

Nonlinear screening leads to fractal electron-hole puddles.

Conductivity depends logarithmically on Coulomb interaction strength.

Charge compressibility and density distribution are characterized in the leading-log approximation.

Abstract

The ground-state and the transport properties of graphene subject to the potential of in-plane charged impurities are studied. The screening of the impurity potential is shown to be nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The conductivity depends logarithmically on $\alpha$, the dimensionless strength of the Coulomb interaction. The theory is asymptotically exact when $\alpha$ is small, which is the case for graphene on a substrate with a high dielectric constant.