Related papers: A Mathematical Theory of Integer Quantum Hall Effe…
In this work, we develop a mathematical theory for the photonic Hall effect and prove the existence of guided electromagnetic waves at the interface of two honeycomb photonic crystals. The guided wave resembles the edge states in electronic…
Degeneracy is an omnipresent phenomenon in various physical systems, which has its roots in the preservation of geometrical symmetry. In electronic and photonic crystal systems, very often this degeneracy can be broken by virtue of strong…
We present an effective theory for the Bloch functions of a two-dimensional square lattice near a quadratic degeneracy point. The degeneracy is protected by the symmetries of the crystal, and breaking these symmetries can either open a…
We present a supersymmetric description of the quantum Hall effect (QHE) in graphene. The noninteracting system is supersymmetric separately at the so-called K and K' points of the Brillouin zone corners. Its essential consequence is that…
A possible realization of Hall conductivity, quantized at odd integer factors of $e^2/h$ for graphene's honeycomb lattice is proposed. I argue that, in the presence of \emph{uniform} real and pseudo-magnetic fields, the valley degeneracy…
By taking into account the charge and spin orderings and the exchange interactions between all the Landau levels, we investigate the integer quantum Hall effect of electrons in graphene using the mean-field theory. At the fillings $\nu =…
The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $\nu=0,\pm 1,\pm 4$ are discovered at magnetic fields…
We numerically study the quantum Hall effect in biased bilayer graphene based on a tight-binding model in the presence of disorder. Integer quantum Hall plateaus with quantized conductivity $\sigma_{xy}=\nu e^2/h$ (where $\nu$ is any…
In this work, we present a mathematical theory for Dirac points and interface modes in honeycomb topological photonic structures consisting of impenetrable obstacles. Starting from a honeycomb lattice of obstacles attaining…
Field-theoretical methods have been shown to be useful in constructing simple effective theories for two-dimensional (2D) systems. These effective theories are usually studied by perturbing around a mean-field approximation, so the question…
The fractional quantum Hall effect is a very particular manifestation of electronic correlations in two-dimensional systems in a strong perpendicular magnetic field. It arises as a consequence of a strong Coulomb repulsion between electrons…
The integer quantum Hall effect is a topological state of quantum matter in two dimensions, and has recently been observed in three-dimensional topological insulator thin films. Here we study the Landau levels and edge states of surface…
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the…
A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal making use of the super cells. The band structure associated with a super cell of a photonic crystal has degeneracies at the edge of the…
We study light-matter interactions in the bulk of a two-dimensional photonic lattice system, where photons are subject to the combined effect of a synthetic magnetic field and an orthogonal synthetic electric field. In this configuration,…
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is…
We investigate the quantum Hall effect in graphene. We argue that in graphene in presence of an external magnetic field there is dynamical generation of mass by a rearrangement of the Dirac sea. We show that the mechanism breaks the lattice…
The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist in principle in the phase transitions involving symmetry protected topological phase, however, examples of such kinds of transition in physical…
There are known two distinct types of the integer quantum Hall effect. One is the conventional quantum Hall effect, characteristic of two-dimensional semiconductor systems, and the other is its relativistic counterpart recently observed in…
Both topological crystalline insulators surfaces and graphene host multi-valley massless Dirac fermions which are not pinned to a high-symmetry point of the Brillouin zone. Strain couples to the low-energy electrons as a time-reversal…