Related papers: Bound states in the continuum: localization of Dir…
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy…
The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them…
We report the formation of bound states in the continuum driven by AC fields. This system consists of a quantum ring connected to two leads. An AC side-gate voltage controls the interference pattern of the electrons passing through the…
We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac…
We study the electronic structure of the junctions between a single graphene layer and carbon nanotubes, using a tight-binding model and the continuum theory based on Dirac fermion fields. The latter provides a unified description of…
We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac…
We demonstrate the existence of localized states in close vicinity of a linear defect in graphene. These states have insulating or conducting character. Insulating states form a flat band, while conducting states present a slowdown of the…
We study localization properties of two-dimensional Dirac fermions subject to a power-law-correlated random vector potential describing, e.g., the effect of "ripples" in graphene. By using a variety of techniques (low-order perturbation…
We explore theoretically the formation of bound states in the continuum (BICs) in graphene hosting two collinear adatoms situated at different sides of the sheet and at the center of the hexagonal cell, where a phantom atom of a fictitious…
We formulate and solve the perhaps simplest two-body bound state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive…
We study a family of local boundary conditions for the Dirac problem corresponding to the continuum limit of graphene, both for nanoribbons and nanodots. We show that, among the members of such family, MIT bag boundary conditions are the…
We study the localized magnetic states of impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene presents the mixing features of Dirac and conventional fermion. For zero…
We consider confinement of Dirac fermions in $AB$-stacked bilayer graphene by inhomogeneous on-site interactions, (pseudo-)magnetic field or inter-layer interaction. Working within the framework of four-band approximation, we focus on the…
Considerable efforts have been made to trap massless Dirac fermions in graphene monolayer, but only quasi-bound states are realized in continuous graphene sheets up to now. Here, we demonstrate the realization of bound states in nanoscale…
We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively…
We show that surface plasmons of a two-dimensional Dirac metal such as graphene can be reflected by line-like perturbations hosting one-dimensional electron states. The reflection originates from a strong enhancement of the local optical…
In the presence of axial magnetic fields that can be realized in deliberately buckled monolayer graphene, quasi-relativistic Dirac fermions may find themselves in a variety of broken symmetry phases even for weak interactions. Through a…
We report on numerical study of the Dirac fermions in partially filled N=3 Landau level (LL) in graphene. At half-filling, the equal-time density-density correlation function displays sharp peaks at nonzero wavevectors $\pm {\bf q^{*}}$.…
Properties of the boundary of two conductors in a quantizing magnetic field are studied: with conventional Dirac charge carriers and so-called pseudospin-1 fermions, which are realized in graphene-like and Lieb lattices respectively. It is…
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…