Related papers: Dirac points for the honeycomb lattice with impene…
We address Anderson localization in disordered honeycomb photonic lattices and show that the localization process is strongly affected by the spectral position of the input wavepacket within the first Brillouin zone of the lattice. In spite…
We study wave propagation in 2D honeycomb structures with a non-commensurate or ``irrational'' line defect or edge. Our model is a Schr\"odinger operator which interpolates, across the edge, between two distinct bulk (asymptotic)…
The absence of screening of the non-local Coulomb interaction in Dirac systems at charge neutrality leads to the breakdown of the Fermi liquid and divergence of the Fermi velocity. On the other hand, Mott Hubbard physics and the concomitant…
This work focuses on the study of the spectral problem for Dirac materials immersed in position-dependent magnetic and electric fields. To achieve this, the system of differential equations satisfied by the eigenfunction components of the…
We study correlations between center vortices and the low-lying eigenmodes of the Dirac operator, in both the overlap and asqtad formulations. In particular we address a puzzle raised some years ago by Gattnar et al. [Nucl. Phys. B 716, 105…
Dirac points in two-dimensional (2D) materials have been a fascinating subject of research, with graphene as the most prominent example. However, the Dirac points in existing 2D materials, including graphene, are vulnerable against…
In this article, we prove that Dirac brackets for Hamiltonian and non-Hamiltonian constrained systems can be derived recursively. We then study the applicability of that formulation in analysis of some interesting physical models.…
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…
We studied numerically electromagnetic response of the finite periodic structure consisting of the ${\cal{PT}}$ dipoles represented by two infinitely long, parallel cylinders with the opposite sign of the imaginary part of a refractive…
The lattice Dirac equation is formulated on a simplicial complex which approximates a smooth Riemann manifold by introducing a lattice vierbein on each site and a lattice spin connection on each link. Care is taken so the construction…
We consider the optical and transport properties in a model two-dimensional Hamiltonian which describes the merging of two Dirac points. At low energy, in the presence of an energy gap parameter $\Delta$, there are two distinct Dirac points…
The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the…
The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated…
We consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions we show that wave-like solutions exist when obstacles (characterized by "holes") are present in 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…
We derive an inequality that relates nodal set and eigenvalues of a class of twisted Dirac operators on closed surfaces and point out how this inequality naturally arises as an eigenvalue estimate for the $\rm Spin^c$ Dirac operator. This…
The one-particle Dirac Hamiltonian with Coulomb interaction is known to be realised, in a regime of large (critical) couplings, by an infinite multiplicity of distinct self-adjoint operators, including a distinguished, physically most…
In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform…
We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…
We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known to show a quantum phase transition…