Bound States in Gapped Graphene with Impurities : Effective Low-Energy Description of Short-Range Interactions

TL;DR

This paper investigates the bound state spectrum of low-energy excitations in gapped graphene with impurities, modeling short-range interactions via boundary conditions and analyzing the Coulomb coupling's behavior.

Contribution

It introduces a novel spectral analysis of impurity-induced bound states in gapped graphene, incorporating boundary conditions to model short-range interactions and exploring renormalization group flow.

Findings

Bound state spectrum depends on boundary conditions.

Spectral properties vary between subcritical and supercritical Coulomb coupling regions.

Renormalization group flow describes Coulomb coupling evolution.

Abstract

We obtain a novel bound state spectrum of the low energy excitations near the Fermi points of graphene in the presence of a charge impurity. The effects of possible short range interactions induced by the impurity are modelled by suitable boundary conditions. The spectrum in the subcritical region of the effective Coulomb coupling is labelled by a parameter which characterizes the boundary conditions and determines the inequivalent quantizations of the system. In the supercritical region we obtain a renormalization group flow for the effective Coulomb coupling.