Scattering in graphene with impurities : A low energy effective theory

TL;DR

This paper develops a low-energy effective theory for impurity scattering in graphene, showing how a single parameter in boundary conditions influences scattering properties and can be empirically determined.

Contribution

It introduces a simplified model using boundary conditions to describe impurity scattering in graphene within the 2D Dirac framework, linking theory to experimental observables.

Findings

Scattering phase shifts depend on a single boundary parameter.

The boundary parameter can be empirically fixed from scattering measurements.

The model applies to both gapless and gapped graphene.

Abstract

We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of the system parameters, the combined effect of the short range interactions due to the charge impurity can be modelled using a single real parameter appearing in the boundary conditions. The phase shifts and the scattering matrix depend explicitly on this parameter. We argue that this parameter for graphene can be fixed empirically, through measurements of observables that depend on the scattering data.