Related papers: A semi-Dirac point in the Hofstadter spectrum
The energies as a function of the magnetic field ($H$) and the pressure are studied theoretically in the tight-binding model for the two-dimensional organic conductor, $\alpha$-(BEDT-TTF)$_2$I$_3$, in which massless Dirac fermions are…
This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is…
Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the…
We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by…
We study the band structure of graphene's Dirac-Weyl quasi-particles in a one-dimensional magnetic superlattice formed by a periodic sequence of alternating magnetic barriers. The spectrum and the nature of the states strongly depend on the…
The properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (delta-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a…
Electrons on honeycomb or pi-flux lattices obey effective massless Dirac equation at low energies and at the neutrality point, and should suffer quantum phase transitions into various Mott insulators and superconductors at strong two-body…
We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T 5 0. At T = 0, we…
We study a functional, whose critical points couple Dirac-harmonic maps from surfaces with a two form. The critical points can be interpreted as coupling the prescribed mean curvature equation to spinor fields. On the other hand, this…
We study the dynamics of ultracold atoms in tailored bichromatic optical lattices. By tuning the lattice parameters, one can readily engineer the band structure and realize a Dirac point, i.e. a true crossing of two Bloch bands. The…
Some important features of the graphene physics can be reproduced by loading ultracold fermionic atoms in a two-dimensional optical lattice with honeycomb symmetry and we address here its experimental feasibility. We analyze in great…
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…
A class of graphene wound into three-dimensional periodic curved surfaces ("graphitic zeolites") is proposed and their electronic structures are obtained to explore how the massless Dirac fermions behave on periodic surfaces. We find in the…
The electronic properties of graphene may be changed from semimetallic to semiconducting by introducing perforations (antidots) in a periodic pattern. The properties of such graphene antidot lattices (GALs) have previously been studied…
We propose a tunable electronic band gap and zero-energy modes in periodic heterosubstrate-induced graphene superlattices. Interestingly, there is an approximate linear relation between the band gap and the proportion of inhomogeneous…
We analyze the energy spectrum of graphene in the presence of spin-orbit coupling and a unidirectionally periodic Zeeman field, focusing on the stability and location of Dirac points it may support. It is found that the Dirac points at the…
In a system with a Dirac-like linear dispersion there are always states that fulfill the resonance condition for electromagnetic radiation of arbitrary frequency $\Omega$. When a flat band is present two kinds of resonant transitions are…
We first point out that the Laia-Tong model realizes the Lieb lattice in the holographic setup. It generates a flat band of sharp particle spectrum together with a Dirac band of unparticle spectrum. We then construct a model which opens a…
The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of…
A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong…