Related papers: Semi-Dirac dispersion relation in photonic crystal…
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…
Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable…
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure--two conical bands touching at a single point--has also been realized for photons in waveguide arrays, atoms in…
We show that a gap parameter can fully describe the merging of Dirac cones in semi-Dirac materials from $K$- and $K^\prime$-points into the common $M$-point in the Brillouin zone. We predict that the gap parameter manifests itself by…
We generalize a proposal by Sorensen et al. [Phys. Rev. Lett. 94, 086803 (2005)] for creating an artificial magnetic field in a cold atom system on a square optical lattice. This leads us to an effective lattice model with tunable spatially…
Different theoretical methods used for the description of diffractive processes in small-x deep inelastic scattering are reviewed. The semiclassical approach, where a partonic fluctuation of the incoming virtual photon scatters off a…
We review the design, theory, and applications of two dimensional periodic lattices hosting conical intersections in their energy-momentum spectrum. The best known example is the Dirac cone, where propagation is governed by an effective…
At photonic Dirac points, electromagnetic waves are governed by the same equations as two-component massless relativistic fermions. However, photonic Dirac points are known to occur in pairs in "photonic graphene" and other similar photonic…
Crystalline symmetries can generate exotic band-crossing features, which can lead to unconventional fermionic excitations with interesting physical properties. We show how a cubic Dirac point---a four-fold-degenerate band-crossing point…
We introduce a general framework for the study of the diffraction of waves by cone points at high frequencies. We prove that semiclassical regularity propagates through cone points with an almost sharp loss even when the underlying operator…
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion…
Klein's paradox refers to the transmission of a relativistic particle through a high potential barrier. Although it has a simple resolution in terms of particle-to-antiparticle tunneling (Klein tunneling), debates on its physical meaning…
A new transport regime of photon in two-dimensional photonic crystal near the Dirac point has been demonstrated by exact numerical simulation. In this regime, the conductance of photon is inversely proportional to the thickness of sample,…
We propose a lattice model for the realization of exotic quartic semi-Dirac fermions, i.e. quasiparticles exhibiting a dispersion with quartic momentum dependence in a given direction, and a linear dependence in the perpendicular direction.…
Dirac semi-metals show a linear electronic dispersion in three dimension described by two copies of the Weyl equation, a theoretical description of massless relativistic fermions. At the surface of a crystal, the breakdown of fermion…
Two-dimensional semimetals with tilted Dirac cones in the electronic band structure are shown to exhibit spatial separation of carriers belonging to different valleys under illumination. In stark contrast to gapped Dirac materials this…
This paper presents a theoretical analysis on bulk and edge states in honeycomb lattice photonic crystals with and without time-reversal and/or space-inversion symmetries. Multiple Dirac cones are found in the photonic band structure and…
Photonic crystals with a two-dimensional triangular lattice have a conical singularity in the spectrum. Close to this so-called Dirac point, Maxwell's equations reduce to the Dirac equation for an ultrarelativistic spin-1/2 particle. Here…
Using the two-dimensional ionic Hubbard model as a simple basis for describing the electronic structure of silicene in the presence of an electric field induced by the substrate, we use the coherent-potential approximation to calculate the…
A theoretical analysis is made of the transformation of the dispersion relation of waves in artificial crystals under the influence of loss, including the case of photonic and phononic crystals. Considering a general dispersion relation in…