A simple model of Coulomb disorder and screening in graphene

Abstract

We suggest a simple model of disorder in graphene assuming that there are randomly distributed positive and negative centers with equal concentration $N/2$ in the bulk of silicon oxide substrate. We show that at zero gate voltage such disorder creates two-dimensional concentration $n_0\sim N^{2/3}$ of electrons and holes in graphene. Electrons and holes reside in alternating in space puddles of the size $R_0\sim N^{-1/3}$. A typical puddle has only one or two carriers in agreement with recent scanning single electron transistor experiment.

2.5 pages, twice longer than previous version

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• Chiral tunneling and the Klein paradox in graphene
• Carrier transport in 2D graphene layers
• A self-consistent theory for graphene transport
• Quantum transport of massless Dirac fermions in graphene
• Electron transport in disordered graphene
• Random resistor network model of minimal conductivity in graphene

Cited by in corpus (15)

• The electronic properties of graphene
• Colloquium: Graphene spectroscopy
• Ground-state of graphene in the presence of random charged impurities
• Boltzmann transport and residual conductivity in bilayer graphene
• Coulomb disorder in three-dimensional Dirac systems
• Anderson Transition in Disordered Graphene
• Theory of the random potential and conductivity at the surface of a topological insulator
• Disorder effects in topological insulator thin films
• Signature of chirality in scanning-probe imaging of charge flow in graphene
• Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers
• Disorder effects in topological insulator nanowires
• Upper bound on the window of density occupied by microemulsion phases in two-dimensional electron systems
• Strange metal phase of disordered magic-angle twisted bilayer graphene at low temperatures: from flatbands to weakly coupled Sachdev-Ye-Kitaev bundles
• Influence of Interface Traps and Electron-Hole Puddles on Quantum Capacitance and Conductivity in Graphene Field-Effect Transistors
• Bound state-continuum resonance transition in a shallow quantum well