Minimal conductivity in graphene: interaction corrections and ultraviolet anomaly

TL;DR

This paper investigates the minimal conductivity of pristine graphene, revealing that interaction corrections are small but depend on ultraviolet regularization, with different calculation methods requiring a proper cutoff.

Contribution

It demonstrates the necessity of ultraviolet cutoff procedures in calculating interaction corrections to graphene's conductivity across multiple methods.

Findings

Interaction correction is approximately 0.01 times the coupling constant g.

Different calculation methods yield inconsistent results without proper ultraviolet regularization.

Ultraviolet cutoff at small distances is essential for consistent conductivity calculations.

Abstract

Conductivity of a disorder-free intrinsic graphene is studied to the first order in the long-range Coulomb interaction and is found to be \sigma=\sigma_0(1+0.01 g), where 'g' is the dimensionless ("fine structure") coupling constant. The calculations are performed using three different methods: i) electron polarization function, ii) Kubo formula for the conductivity, iii) quantum transport equation. Surprisingly, these methods yield different results unless a proper ultraviolet cut-off procedure is implemented, which requires that the interaction potential in the effective Dirac Hamiltonian is cut-off at small distances (large momenta).