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.

arXiv comment2.5 pages, twice longer than previous version

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• Colloquium: Graphene spectroscopy
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• Boltzmann transport and residual conductivity in bilayer graphene
• Coulomb disorder in three-dimensional Dirac systems
• Neutrality point of graphene with coplanar charged impurities
• Quantum Hall effect in exfoliated graphene affected by charged impurities: metrological measurements
• Anderson Transition in Disordered Graphene
• Theory of the random potential and conductivity at the surface of a topological insulator
• Interface states and anomalous quantum oscillations in graphene hybrid structures
• Van der Waals heterostructures with spin-orbit coupling
• Disorder effects in topological insulator thin films
• Electronic transport, metal-insulator transition, and Wigner crystallization in transition metal dichalcogenide monolayers
• Signature of chirality in scanning-probe imaging of charge flow in graphene
• 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
• Rodlike counterions at heterogeneously charged surfaces
• 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