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Specific properties, such as surface Fermi arcs, features of quantum oscillations and of various responses to a magnetic field, distinguish Dirac semimetals from ordinary materials. These properties are determined by Dirac points at which a…
Using an evolutionary algorithm in combination with first-principles density functional theory calculations, we identify two-dimensional (2D) CaP$_3$ monolayer as a new Dirac semimetal due to inversion and nonsymmorphic spatial symmetries…
The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical…
Epitaxial graphene, grown on SiC(0001) surface, has been widely studied both experimentally and theoretically. It was found that first epitaxial graphene layer in such structures is a buffer layer i.e. there are no characteristic Dirac…
Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most…
Weyl and Dirac semimetals are three dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three dimensional analogs of graphene, they have generated much recent interest. Deep…
In a Dirac semimetal, the conduction and valence bands contact only at discrete (Dirac) points in the Brillouin zone (BZ) and disperse linearly in all directions around these critical points. Including spin, the low energy effective theory…
The behaviour of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, where two one-dimensional Schr\"{o}dinger Hamiltonians $H^{\pm}$ are…
We study the Quantum Electrodynamics of 2D and 3D Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb…
The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times…
Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the two-dimensional material, enhance electron correlations, and give rise to novel condensed-matter…
The paper reports a theoretical study of scattering of electrons by edges in graphene and its effect on Raman scattering. First, effective models are discussed for translationally invariant and rough edges. Second, they are used in a…
Bilayer graphene twisted by a small angle shows a significant charge modulation away from neutrality, as the charge in the narrow bands near the Dirac point is mostly localized in the regions of the Moir\'e pattern with $AA$ stacking. The…
Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional electron systems and, ultimately, create materials with tailored electronic properties. Previously, it proved difficult to…
Fabrication of graphene structures has triggered vast research efforts focused on the properties of two-dimensional systems with massless Dirac fermions. Nevertheless, further progress in exploring this quantum electrodynamics system in…
There is evidence for existence of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. It is shown that…
The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i)…
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only…
After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…
The family of solutions to the Dirac equation for an electron moving in an electromagnetic lattice with the chiral structure created by counterpropagating circularly polarized plane electromagnetic waves is obtained. At any nonzero…