Related papers: Fullerenes, Zero-modes, and Self-adjoint Extension…
Recent studies have focused on laser-induced gaps in graphene which have been shown to have a topological origin, thereby hosting robust states at the sample edges. While the focus has remained mainly on these topological chiral edge…
The gap equation for Dirac quasiparticles in monolayer graphene in constant magnetic and pseudomagnetic fields, where the latter is due to strain, is studied in a low-energy effective model with contact interactions. Analyzing solutions of…
The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical…
We consider plane junctions with graphene electrodes, which are formed by a single-level system ("molecule") placed between the edges of two single-layer graphene half planes. We calculate the edge Green functions of the electrodes and the…
Anderson's orthogonality catastrophe in graphene, at energies close to the Dirac point, is analyzed. It is shown that, in clean systems, the orthogonality catastrophe is suppressed, due to the vanishing density of states at the Dirac point.…
We present a simple analytical approach to study anharmonic effects in single layer, bilayer, and multilayer graphene. The coupling between in plane and out of plane modes leads to negative Gr\"uneisen coefficients and negative thermal…
The electronic properties of a bricklayer model, which shares the same topology as the hexagonal lattice of graphene, are investigated numerically. We study the influence of random magnetic-field disorder in addition to a strong…
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by…
These lecture notes focus on the bound state sector of QCD. Motivated by data which suggests that the strong coupling \alpha_s(Q) freezes at low Q, and by similarities between the spectra of hadrons and atoms, I discuss if and how QCD bound…
This paper is devoted to the construction of semiclassical spectrum and efficient (simple to implement) explicit semiclassical asymptotic eigenfunctions of the Dirac operator for relatively high-energy bound states in graphene in magnetic…
Electronic eigen-states of a square graphene quantum dot(GQD) terminated by both zigzag and armchair edges are derived in the theoretical framework of Dirac equation. We find that the Dirac equation can determine the eigen-energy spectrum…
We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction f=1/3 interacting through a nearest-neighbor interaction V. Above a critical interaction strength V_c a charge-density wave with a broken…
We consider a square lattice configuration of circular gate-defined quantum dots in an unbiased graphene sheet and calculate the electronic, particularly spectral properties of finite albeit actual sample sized systems by means of a…
A model in which a Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor…
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…
The Klein paradox, first introduced in relation to chiral tunneling, is also manifested in the study of bound-states in single-layer graphene with a 1D square-well potential. We derive analytic (and numerical) solutions for bound-state…
A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved…
In order to manipulate the properties of graphene, its very important to understand the electronic structure in presence of disorder. We investigate, within a tight-binding description, the effects of disorder in the on-site (diagonal…
The dynamical conductivity of interacting multiband electronic systems derived in Ref.[1] is shown to be consistent with the general form of the Ward identity. Using the semiphenomenological form of this conductivity formula, we have…
We investigate the superconducting proximity effect through graphene in the long diffusive junction limit, at low and high magnetic field. The interface quality and sample phase coherence lead to a zero resistance state at low temperature,…