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

Abstract

We characterize the carrier density profile of the ground state of graphene in the presence of particle-particle interaction and random charged impurity for 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 resulting 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 (2D) random-field surfaces.

arXiv comment12 pages, 10 figures

References in corpus (32)

• Electronic transport in two dimensional graphene
• Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor
• Atomic Structure of Graphene on SiO2
• Carrier transport in 2D graphene layers
• A self-consistent theory for graphene transport
• Quantum Hall Ferromagnetism in Graphene
• Origin of Spatial Charge Inhomogeneity in Graphene
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• SLE for theoretical physicists
• Graphene as an electronic membrane
• Scanning tunneling spectroscopy of inhomogeneous electronic structure in monolayer and bilayer graphene on SiC
• Spatially resolved spectroscopy of monolayer graphene on SiO2
• Chirality and Correlations in Graphene
• Charge Transport and Inhomogeneity near the Charge Neutrality Point in Graphene
• Effect of electron-electron interactions on the conductivity of clean graphene
• Conformal Field Theories of Stochastic Loewner Evolutions
• Ground-state of graphene in the presence of random charged impurities
• Density-Functional Theory of Graphene Sheets
• Effect of disorder on a graphene p-n junction
• Density dependent exchange contribution to $\partial \mu /\partial n$ in extrinsic graphene
• Nonlinear Measures for Characterizing Rough Surface Morphologies
• Anomalous thermodynamics of Coulomb interacting massless Dirac fermions in two spatial dimensions
• Mapping the Dirac point in gated bilayer graphene
• Watersheds are Schramm-Loewner Evolution curves
• Imaging coherent transport in graphene (Part II): Probing weak localization
• Kaon vs. Bottom: Where to look for a general MSSM?
• Statistical Topography of Glassy Interfaces
• Observation of SLE$(\kappa ,\rho )$ on the Critical Statistical Models
• Conformal Invariance of Graphene Sheets
• Contour lines of the discrete scale invariant rough surfaces
• Geometrical exponents of contour loops on synthetic multifractal rough surfaces: multiplicative hierarchical cascade p-model
• Fokker-Planck Equation of Schramm-Loewner Evolution

Cited by in corpus (4)

• Statistical Investigation of Avalanches of Three Dimensional Small-World Networks and their Boundary and Bulk Cross-Sections
• Gaussian Free Field in the iso-height random islands tuned by percolation model
• Sandpile on uncorrelated site-diluted percolation lattice; From three to two dimensions
• Scaling properties of mono-layer graphene away from the Dirac point