Related papers: A semi-Dirac point in the Hofstadter spectrum
We review the energy spectrum and transport properties of several types of one- dimensional superlattices (SLs) on single-layer and bilayer graphene. In single-layer graphene, for certain SL parameters an electron beam incident on a SL is…
We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at…
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide…
Weak topological insulators and Dirac semimetals are gapped and nodal phases with distinct topological properties, respectively. Here, we propose a novel topological phase that exhibits features of both and is dubbed composite Dirac…
Tight binding models like the Hubbard Hamiltonian are most often explored in the context of uniform intersite hopping $t$. The electron-electron interactions, if sufficiently large compared to this translationally invariant $t$, can give…
We study strongly correlated fractional topological phases on a two-sphere threaded by a magnetic dipole field with globally vanishing flux. Solving the Dirac equation in this background produces spheroidal wavefunctions forming a highly…
We study a class of Dirac semimetals that feature an eightfold-degenerate double Dirac point. We show that 7 of the 230 space groups can host such Dirac points and argue that they all generically display linear dispersion. We introduce an…
The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks…
After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…
We show that in superlattices with a strong band inversion no hybridization gap exists. There are two points where the bands are crossing and the spectrum has a shape of Dirac cones. Due to the absence of the hybridization gap the optical…
In the present work, we give a phenomenological theory of the monolayer graphene where two worlds quantum and classical meet together and complete each other in the most natural way. It appears that the graphene is the unique material where…
By deriving a tight-binding model, we demonstrate a mechanism of forming a nodal line of Dirac points in a single-component molecular conductor [Pt(dmtd)$_2$] [Zhou {\it et al.}, Chem. Commun. {\bfseries 55}, 3327 (2019)], consisting of…
Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not…
We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical…
Three-dimensional topological semimetals come in different variants, either containing Weyl points or Dirac lines. Here we describe a more complicated momentum-space topological defect where several separate Dirac lines connect with each…
Emergent Dirac fermions provide the starting point to understanding the plethora of novel condensed matter phases. The nature of the associated phases and phase transitions crucially depends on both the emergent symmetries as well as the…
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…
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\neq 0, in the case of…
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…
We study the band structure of electrons hopping on a honeycomb lattice with 1/q (q integer) flux quanta through each elementary hexagon. In the nearest neighbor hopping model the two bands that eventually form the n = 0 Landau level have…