Related papers: Tunable Dirac points in a two-dimensional non-symm…
Recent developments in the relationship between bulk topology and surface crystal symmetry have led to the discovery of materials whose gapless surface states are protected by crystal symmetries. In fact, there exists only a very limited…
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…
Starting from the nearest-neighbor tight-binding model on {10,3} and {14,3} hyperbolic lattices that, for a uniform hopping amplitude, gives rise to emergent Dirac fermions on a curved space with a constant negative curvature, displaying a…
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…
Dirac materials have unique transport properties, partly due to the presence of surface states. A new type of Dirac materials, protected by non-symmorphic symmetries was recently proposed by Young and Kane [1]. By breaking of time reversal…
Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing…
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…
The Dirac fermion with linear dispersion in the kagom\'e lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry…
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…
Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in…
Dirac cones (DCs) play a pivotal role in various unique phenomena ranging from massless electrons in graphene to robust surface states in topological insulators (TIs). Recent studies have theoretically revealed a full Dirac hierarchy…
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…
The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap…
We study effects of strain on the electronic properties of the kagome lattice in a tight-binding formalism with spin-orbit coupling (SOC). The degeneracy at the $\Gamma$ point evolves into a pair of emergent tilted Dirac cones under…
Materials harboring exotic quasiparticles, such as Dirac and Weyl fermions\cite{xu2015discovery,borisenko2015time,weng2015weyl,xu2015observation}, have garnered much attention from the physics and material science communities. These…
The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One…
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…
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice. We investigate the topological properties of a silicene superstructure generated by an external periodic potential. The superstructure is a quantum…
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…
We consider the vortex state of d-wave superconductors in the clean limit. Within the linearized approximation the quasiparticle bands obtained are found to posess Dirac cone dispersion (band touchings) at special points in the Brillouin…