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Scale-invariant puddles in graphene: Geometric properties of electron-hole distribution at the Dirac point

M. N. Najafi1,* and M. Ghasemi Nezhadhaghighi2

  • 1Department of Physics, University of Mohaghegh Ardabili, P. O. Box 179, Ardabil, Iran
  • 2Department of Physics, College of Science, Shiraz University, Shiraz 71454, Iran

  • *morteza.nattagh@gmail.com
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Phys. Rev. E 95, 032112 – Published 7 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.032112

Abstract

We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity in zero gate voltage. We provide detailed analysis on the resulting spatially inhomogeneous electron gas, taking into account the particle-particle interaction and the remote Coulomb disorder on an equal footing within the Thomas-Fermi-Dirac theory. We present some general features of the carrier density probability measure of the graphene sheet. We also show that, when viewed as a random surface, the electron-hole puddles at zero chemical potential show peculiar self-similar statistical properties. Although the disorder potential is chosen to be Gaussian, we show that the charge field is non-Gaussian with unusual Kondev relations, which can be regarded as a new class of two-dimensional random-field surfaces. Using Schramm-Loewner (SLE) evolution, we numerically demonstrate that the ungated graphene has conformal invariance and the random zero-charge density contours are SLEκ with κ=1.8±0.2, consistent with c=−3 conformal field theory.

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Phys. Rev. E 95, 032112– Published 7 March, 2017
  • Received 17 October 2016

©2017 American Physical Society

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