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

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.

Complex Supersymmetry in Graphene

“…To solve the Dirac equation ( 15) for a massless particle, we first decouple the system of equations that the components of Ψ 0,n = (ψ + 0,n , ψ − 0,n ) T fulfill, see Eqs. ( 18) and (19). Both components satisfy the Schrödinger Eqs.…”

“…To confine or control the charge carriers in a graphene sample, electromagnetic fields have to be applied [11][12][13][14]; it has been shown that mechanical deformations can be used as well for that purpose [15][16][17][18][19]. To explore and enrich the configurations where the Dirac equation can be solved exactly (or quasiexactly), supersymmetric quantum mechanics have been used from different approaches [20][21][22][23][24][25][26][27][28][29][30][31][32].…”

Effect of Coulomb impurities on the electronic structure of magic angle twisted bilayer graphene

“…To date, most experimental and theoretical works have focused on understanding the properties of pristine tBLG, but it is well known that defects play an important role in real devices that exploit the properties of two-dimensional (2D) materials 11,32 . In particular, impurities that donate electrons or holes can be used to control the concentration of charge carriers [33][34][35][36][37][38][39] . Once ionized, these impurities act as Coulomb scatterers and reduce the charge carrier mobility 40 .…”