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Introducing quasiparticle anisotropy in graphene via uniaxial strain has a profound effect on the polarization charge density induced by external impurities, both Coulomb and short-range. In particular, the charge distribution induced by a…
We reveal a new type of supercritical behavior in gapped graphene with two oppositely charged impurities by studying the two-dimensional Dirac equation for quasiparticles with the Coulomb potential regularized at small distances accounting…
We review the theoretical and experimental results connected with the electron states in two-dimensional Dirac systems paying a special attention to the atomic collapse in graphene. Two-electron bound states of a Coulomb impurity are…
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…
We explore the problem of atomic collapse in graphene by monopole impurities, both electric and magnetic, within the context of supersymmetric quantum mechanics. For electric impurities, upon factorizing the radial Dirac Hamiltonian and…
We study electric dipole effects for massive Dirac fermions in graphene and related materials. The dipole potential accomodates towers of infinitely many bound states exhibiting a universal Efimov-like scaling hierarchy. The dipole moment…
We theoretically consider the effect of plasmon collective modes on the frequency-dependent conductivity of graphene in the presence of the random static potential of charged impurities. We develop an equation of motion approach suitable…
We study the Dirac equation for quasiparticles in gapped graphene with two oppositely charged impurities by using the technique of linear combination of atomic orbitals and variational Galerkin--Kantorovich method. We show that for…
We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi…
Screening of charge impurities in graphene is analyzed using the exact solution for vacuum polarization obtained from the massless Dirac-Kepler problem. For the impurity charge below certain critical value no density perturbation is found…
The electronic energy spectrum of graphene electron subjected to a homogeneous magnetic field in the presence of a charged Coulomb impurity is studied analytically within two-dimensional Dirac-Weyl picture by using variational approach. The…
We study the problem of the electron excitation spectrum in the presence of point-like and regularized Coulomb impurities in gapped graphene. To this end, we use the Dirac model and in the point-like case theory of self-adjoint extensions…
The relevance of the strain-induced Dirac point shift to obtain the appropriate anisotropic Fermi velocity of strained graphene is demonstrated. Then a critical revision of the available effective Dirac Hamiltonians is made by studying in…
We have investigated a new feature of impurity cyclotron resonances common to various localized potentials of graphene. A localized potential can interact with a magnetic field in an unexpected way in graphene. It can lead to formation of…
The electric conductance of a strip of undoped graphene increases in the presence of a disorder potential, which is smooth on atomic scales. The phenomenon is attributed to impurity-assisted resonant tunneling of massless Dirac fermions.…
We obtain a novel bound state spectrum of the low energy excitations near the Fermi points of graphene in the presence of a charge impurity. The effects of possible short range interactions induced by the impurity are modelled by suitable…
We consider the problem of electron energy states related to strongly localized potential of a single impurity in graphene. Our model simulates the effect of impurity atom substituting the atom of carbon, on the energy spectrum of electrons…
The electrical conductivity of graphene containing point defects is studied within the binary alloy model in its dependence on the Fermi level position at the zero temperature. It is found that the minimal conductivity value does not have a…
We evaluate the autocorrelation function of the electrostatic potential in doped graphene due to nearby charged impurities. The screening of those impurities is described by a combination of the polarization function for graphene in random…
We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Green's function of the Dirac fermions in the…