Accumulation Rate of Bound States of Dipoles Generated by Point Charges in Strained Graphene

TL;DR

This paper investigates how bound state energies in strained graphene with specific charge distributions accumulate rapidly at the spectral gap edges, providing precise accumulation rate estimates.

Contribution

It introduces a detailed analysis of bound state accumulation in strained graphene modeled by the massive Dirac operator with complex charge configurations.

Findings

Bound states accumulate exponentially fast at spectral gap edges.

The leading order of accumulation rate is explicitly determined.

Charge distributions with vanishing total charge and non-zero dipole moment are analyzed.

Abstract

We consider strained graphene, modelled by the two-dimensional massive Dirac operator, with potentials corresponding to charge distributions with vanishing total charge, non-vanishing dipole moment and finitely many point charges of subcritical coupling constants located in the graphene sheet. We show that the bound state energies accumulate exponentially fast at the edges of the spectral gap by determining the leading order of the accumulation rate.