Related papers: Electrical dipole on gapped graphene: Bound states…

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…

Coupled electron-hole states are realized in a system consisting of a combination of an electrostatic potential barrier and ring-shaped potential well, which resembles a circular dipole. A perpendicular magnetic field induces confined…

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…

The electronic bound states and resonances in the vicinity of the Dirac point energy due to the adsorption of calcium dimers on a suspended graphene monolayer are explored theoretically using density functional theory (DFT) and an improved…

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 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…

Atomic collapse in graphene nanoribbons behaves in a fundamentally different way as compared to monolayer graphene, due to the presence of multiple energy bands and the effect of edges. For armchair nanoribbons we find that bound states…

The effect of substitution atoms on the energy spectrum and the electrical conductivity of graphene was investigated in a Lifshitz one-electron tight-binding model. It is established that the ordering of impurity atoms results in a gap in…

We consider strained graphene, modelled by the two-dimensional massive Dirac operator, with potentials corresponding to charge distributions with vanishing total charge, non-vanishing dipole moment and finitely many point charges of…

We analyse the interaction between charges and graphene layers. The electric polarisability of graphene induces a force, that can be described by an image charge. The analysis shows that graphene can be described as an imperfect conductor…

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 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…

We show that in graphene charge distributions with non-vanishing dipole moment have infinitely many bound states. The corresponding eigenvalues accumulate at the edges of the gap faster than any power.

It is demonstrated that there is a characteristic impurity concentration, at which variation with concentration and overall appearance of the local density of states at the impurity site in graphene are changing their behavior. Features…

The electronic energy gap and total dipole moment of chemically functionalized hexagonal and triangular graphene quantum dots are investigated by the density functional theory. It has been found that the energy gap can be efficiently tuned…

We present a quantum analysis of the massless excitations in graphene with a charge impurity. When the effective charge exceeds a certain critical value, the spectrum is quantized and is unbounded from below. The corresponding eigenstates…

Atomic collapse is a phenomenon inherent to relativistic quantum mechanics where electron states dive in the positron continuum for highly charged nuclei. This phenomenon was recently observed in graphene. Here we investigate a novel…

The modification of the quantum states in a Dice lattice due to a Coulomb impurity are investigated. The energy band structure of a pristine Dice lattice consists of a Dirac cone and a flat band at the Dirac point. We use the tight binding…

We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential delimited in an infinite graphene…

Resonant scattering at the atomic absorbates in graphene was investigated recently in relation with the transport and gap opening problems. Attaching an impurity atom to graphene is believed to lead to the creation of unusual zero energy…