Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities

TL;DR

This paper investigates the ground-state energy and scattering behavior of Dirac fermions in gapped graphene with two Coulomb impurities, using LCAO and nonperturbative methods for different impurity charge configurations.

Contribution

It introduces a combined approach to analyze ground-state energies and scattering in graphene with Coulomb impurities, covering equal and opposite charge cases.

Findings

Ground-state energy analyzed with LCAO for equal charges.

Nonperturbative scattering analysis for opposite charges.

Insights into impurity effects on graphene's electronic properties.

Abstract

We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.