Electronic Structure of gated graphene and graphene ribbons

TL;DR

This paper investigates how gating affects the electronic properties of graphene and graphene ribbons, including carrier density, subband occupation, and conductance, using self-consistent calculations.

Contribution

It provides a detailed analysis of Coulomb interactions and quantum effects in gated graphene structures, including threshold voltages and conductance behavior.

Findings

Conductance of wide ribbons scales with the square root of gate voltage.

Quantum corrections modify classical capacitance estimates.

Identified threshold voltages for conduction in semiconducting ribbons.

Abstract

We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers, $n_{2D}$, the number of occupied subbands and the density profiles as a function of the gate potential $V_g$. We discuss quantum corrections to the classical capacitance and we calculate the threshold $V_g$ above which semiconducting armchair ribbons conduct. We find that the ideal conductance of perfectly transmitting wide ribbons is proportional to the square root of the gate voltage.