Critical behavior for point monopole and dipole electric impurities in uniformly and uniaxially strained graphene

Julio César Pérez-Pedraza,Erik Díaz-Bautista,Alfredo Raya,David Valenzuela

doi:10.1103/physrevb.102.045131

Abstract

We revisit the problem of bound states in graphene under the influence of point electric monopole and dipole impurity potentials extended to the case in which the membrane of this material is uniformly and uniaxially strained, which leads to a redefinition of the charge and dipole moment, respectively. By considering an anisotropic Fermi velocity, we analytically solve the resulting Dirac equation for each potential. We observe that the effect of the anisotropy is to promote or inhibit the critical behavior known to occur for each kind of impurity, depending on the direction along which strain is applied: both the atomic collapse, for the monopole impurity, and the emergence of cascades of infinitely many bound states with a universal Efimov-like scaling, for the dipole impurity, are phenomena that occur under less or more restrictive conditions due to strain.

Highlights

Ever since the isolation of graphene samples in 2004 [1], this material has played a leading role in exploring analogs and similarities of phenomena occurring in different branches of physics
We revisit the problem of bound states in graphene under the influence of point electric monopole and dipole impurity potentials extended to the case in which the membrane of this material is uniformly and uniaxially strained, which leads to a redefinition of the charge and dipole moment, respectively
In this paper we have carried out an analysis of the bound states for the anisotropic 2D Dirac equation in the potential of point electric monopole and dipole impurities in the context of graphene physics

Summary

INTRODUCTION

Ever since the isolation of graphene samples in 2004 [1], this material has played a leading role in exploring analogs and similarities of phenomena occurring in different branches of physics. This theoretical prediction was experimentally confirmed [17] by using the tip of a scanning tunneling microscope (STM) to create clusters of charged calcium dimmers, creating a supercritically charged Coulomb potential from subcritical charges (as in heavy-ion collisions) In these experiments, a systematic electron-hole asymmetry owing to the positive charge of the dimmers was observed, along with the appearance of a resonance (a quasibound state) increasing and shifting toward lower energies as the number of dimmers increased from one to five. By solving the corresponding anisotropic Dirac equation under the influence of monopole and dipole electric impurity potentials, we explore the role of the anisotropy in the critical thresholds for these problems For this purpose, we have organized the remainder of this paper as follows: we solve the anisotropic Dirac equation for the case of a monopole electric impurity immersed in a uniform magnetic field [34] and explore the behavior of the bound-state energies.

MONOPOLE IMPURITY AND MAGNETIC FIELD IN STRAINED GRAPHENE

Collapse without external magnetic field

Collapse including magnetic field

POINT DIPOLE IN STRAINED GRAPHENE

CONCLUSIONS