Related papers: Dirac cones for point scatterers on a honeycomb la…
Zirconium pentatelluride was recently reported to be a 3D Dirac semimetal, with a single conical band, located at the center of the Brillouin zone. The cone's lack of protection by the lattice symmetry immediately sparked vast discussions…
The electronic spectrum of sheets of graphite (plane honeycomb lattice) folded into regular polihedra is studied. A continuum limit valid for sufficiently large molecules and based on a tight binding approximation is derived. It is found…
We propose a technique to realize a tachyonic band structure in a coherent network, such as an array of coupled ring resonators. This is achieved by adding "PT symmetric" spatially-balanced gain and loss to each node of the network. In a…
Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of…
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…
We present a combined angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations study of the electronic structure of LaAgSb$_2$ in the entire first Brillouin zone. We observe a Dirac-cone-like structure in the…
Graphene, a honeycomb lattice of carbon atoms ruled by tight-binding interaction, exhibits extraordinary electronic properties due to the presence of Dirac cones within its band structure. These intriguing singularities have naturally…
We have realized different honeycomb lattices for microwave photons in the 4 to 8 GHz band using superconducting spiral resonators. Each lattice comprises a few hundred sites. Two designs have been studied, one leading to two bands touching…
Semiconductor superlattices may display dispersions that are degenerate either at the zone center or zone boundary. We show that they are linear upon the wave-vector in the vicinity of the crossing point. This establishes a realisation of…
We provide a novel setup for generalizing the two-dimensional pseudospin S=1/2 Dirac equation, arising in graphene's honeycomb lattice, to general pseudospin-S. We engineer these band structures as a nearest-neighbor hopping Hamiltonian…
General properties of long wavelength triangular graphene superlattice are studied. It is shown that Dirac points with and without gaps can arise at a number of high symmetry points of the Brillouin Zone. The existence of gaps can lead to…
The energy spectra for the tight-binding models on the Lieb and kagom\'e lattices both exhibit a flat band. We present a model which continuously interpolates between these two limits. The flat band located in the middle of the three-band…
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…
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…
The Schr\"odinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of band gaps near points of the reciprocal lattice known as Brillouin zone boundaries. However, in…
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…
The collective electronic properties of various types of pseudospin-$1$ Dirac-cone materials with a flat band and finite bangaps in their energy spectra are the subject of our reported investigation. Specifically, we have calculated the…
We demonstrate how a Dirac-like magnon spectrum is generated for localized magnetic moments forming a two-dimensional honeycomb lattice. The Dirac crossing point is proven to be robust against magnon-magnon interactions, as these only shift…
We study the dynamics of coherent waves in nonlinear honeycomb lattices and show that nonlinearity breaks down the Dirac dynamics. As an example, we demonstrate that even a weak nonlinearity has major qualitative effects one of the…
In conventional lattice models, the dispersion relation $\omega(k)$ is assumed to be a smooth function which is periodic over the first Brillouin Zone. However, in subwavelength atom arrays the dispersion of the light-mediated long-range…