A comprehensive study of electric, thermoelectric and thermal conductivities of Graphene with short range unitary and charged impurities

TL;DR

This paper provides a detailed theoretical analysis of electrical and thermal conductivities in graphene with impurities, comparing results with experimental data and highlighting the complex influence of impurity types on transport properties.

Contribution

It offers a comprehensive, self-consistent calculation of transport properties in graphene considering both unitary and charged impurities, with analytic expressions and experimental comparisons.

Findings

Qualitative agreement with experimental temperature and density dependence.

Impurity parameters can fit some transport measurements but not all simultaneously.

Different impurity models fit different sets of transport data.

Abstract

Motivated by the experimental measurement of electrical and hall conductivity, thermopower and Nernst effect, we calculate the longitudinal and transverse electrical and heat transport in graphene in the presence of unitary scatterers as well as charged impurities. The temperature and carrier density dependence in this system display a number of anomalous features that arise due to the relativistic nature of the low energy fermionic degrees of freedom. We derive the properties in detail including the effect of unitary and charged impurities self-consistently, and present tables giving the analytic expressions for all the transport properties in the limit of small and large temperature compared to the chemical potential and the scattering rates. We compare our results with the available experimental data. While the qualitative variations with temperature and density of carriers or chemical potential of all transport properties can be reproduced, we find that a given set of parameters of the impurities fits the Hall conductivity, Thermopower and the Nernst effect quantitatively but cannot fit the conductivity quantitatively. On the other hand a single set of parameters for scattering from Coulomb impurities fits conductivity, hall resistance and thermopower but not Nernst.