Sum Rules for the Optical and Hall Conductivity in Graphene

TL;DR

This paper derives sum rules for optical and Hall conductivity in graphene, revealing unique dependencies on gate voltage and temperature due to its Dirac-like quasiparticles, with implications for understanding its electronic properties.

Contribution

It introduces novel sum rules for graphene's optical and Hall conductivities, accounting for interband transitions and Dirac quasiparticle effects, which differ from conventional materials.

Findings

Spectral weight dependence on gate voltage as ~const - |V_g|^{3/2}

Temperature dependence of spectral weight as T^3 at V_g=0

Hall frequency proportional to carrier imbalance density and V_g

Abstract

Graphene has two atoms per unit cell with quasiparticles exhibiting the Dirac-like behavior. These properties lead to interband in addition to intraband optical transitions and modify the $f$-sum rule on the longitudinal conductivity. The expected dependence of the corresponding spectral weight on the applied gate voltage $V_g$ in a field effect graphene transistor is $\sim {const}- |V_g|^{3/2}$. For $V_g =0$, its temperature dependence is $T^3$ rather than the usual $T^2$. For the Hall conductivity, the corresponding spectral weight is determined by the Hall frequency $\omega_H$ which is linear in the carrier imbalance density $\rho$, and hence proportional to $V_g$, and is different from the cyclotron frequency for Dirac quasiparticles.