Accumulation Rate of Bound States of Dipoles in Graphene

TL;DR

This paper proves that the energies of bound states caused by dipole potentials in graphene accumulate exponentially fast at the band edge of the two-dimensional massive Dirac operator.

Contribution

It provides a rigorous proof of the exponential accumulation rate of bound state energies, extending previous results by De Martino et al. (2014).

Findings

Bound state energies accumulate exponentially at the band edge.

The paper confirms a formula previously suggested by De Martino et al. (2014).

Provides mathematical proof for the accumulation rate in graphene models.

Abstract

We prove that the bound state energies of the two-dimensional massive Dirac operator with dipole type potentials accumulate with exponentials rate at the band edge. In fact we prove a corresponding formula of De Martino et al (2014).