Electrical dipole on gapped graphene: Bound states and atomic collapse

TL;DR

This study explores how an electrical dipole on gapped graphene creates bound states and atomic collapse phenomena, revealing how energy levels evolve with charge strength and dipole size, and how these states transition from single-impurity to dipole configurations.

Contribution

It provides a detailed analysis of bound states, anticrossings, and atomic collapse in gapped graphene with an electrical dipole, extending understanding of impurity effects in such materials.

Findings

Bound states exist within the gap region.

Energy levels exhibit anticrossings and crossings as a function of charge strength.

States transition into atomic collapse states when entering the continuum.

Abstract

We investigate the energy spectrum, wave functions, and local density of states of an electrical dipole placed on a sheet of gapped graphene as function of the charge strength Z{\alpha} for different sizes of the dipole and for different regularization parameters. The dipole is modeled as consisting of a positive and negative charge. Bound states are found within the gap region with some energy levels that anticross and others that cross as function of the impurity strength Z{\alpha}. The anticrossings are more pronounced and move to higher charges Z{\alpha} when the length of the dipole decreases. These energy levels turn into atomic collapse states when they enter the positive (or negative) energy continuum. A smooth transition from the single-impurity behavior to the dipole one is observed: The states diving towards the continuum in the single-impurity case are gradually replaced by a series of anticrossings that represent a continuation of the diving states in the single-impurity case. By studying the local density of states at the edge of the dipole we show how the series of anticrossings persist in the positive and negative continuum.