Conductivity of suspended and non-suspended graphene at finite gate voltage

TL;DR

This paper calculates the DC and optical conductivity of graphene at finite chemical potential, considering disorder and phonon effects, and compares results with experimental data, highlighting the impact of impurities and substrate conditions.

Contribution

It provides a comprehensive theoretical framework for graphene conductivity including disorder and phonon effects, aligning with experimental observations.

Findings

Qualitative agreement with recent experiments

Disorder effects are significant in conductivity behavior

Water molecules under graphene influence quantitative results

Abstract

We compute the DC and the optical conductivity of graphene for finite values of the chemical potential by taking into account the effect of disorder, due to mid-gap states (unitary scatterers) and charged impurities, and the effect of both optical and acoustic phonons. The disorder due to mid-gap states is treated in the coherent potential approximation (CPA, a self-consistent approach based on the Dyson equation), whereas that due to charged impurities is also treated via the Dyson equation, with the self-energy computed using second order perturbation theory. The effect of the phonons is also included via the Dyson equation, with the self energy computed using first order perturbation theory. The self-energy due to phonons is computed both using the bare electronic Green's function and the full electronic Green's function, although we show that the effect of disorder on the phonon-propagator is negligible. Our results are in qualitative agreement with recent experiments. Quantitative agreement could be obtained if one assumes water molelcules under the graphene substrate. We also comment on the electron-hole asymmetry observed in the DC conductivity of suspended graphene.