Dynamical diffusion and renormalization group equation for the Fermi velocity in doped graphene

TL;DR

This paper investigates electron transport in doped graphene, deriving response functions and a renormalization group equation for the Fermi velocity, revealing how impurities affect electronic properties.

Contribution

It introduces a generalized response theory for graphene with impurities and derives a renormalization group equation for the Fermi velocity up to second order.

Findings

Minimum conductivity in no-disorder limit

Exact relation between response functions

Renormalization group equation for Fermi velocity

Abstract

The aim of this work is to study the electron transport in graphene with impurities by introducing a generalization of linear response theory for linear dispersion relations and spinor wave functions. Current response and density response functions are derived and computed in the Boltzmann limit, showing that in the former case, a minimum conductivity appears in the no-disorder limit. In turn, from the generalization of both functions, an exact relation can be obtained that relates both. Combining this result with the relation given by the continuity equation, it is possible to obtain general functional behavior of the diffusion pole. Finally, a dynamical diffusion is computed in the quasistatic limit using the definition of relaxation function. A lower cutoff must be introduced to regularize infrared divergences, which allow us to obtain a full renormalization group equation for the Fermi velocity, which is solved up to order O(h^2).