Related papers: A Mathematical Theory of Integer Quantum Hall Effe…
It is well known that band inversion across a straight interface in a periodic medium gives rise to interface modes that are localized near the interface and propagate along it inside the bulk spectral gap. This phenomenon constitutes the…
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through…
When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids…
We consider interacting bosonic atoms in an optical lattice subject to a large simulated magnetic field. We develop a model similar to a bilayer fractional quantum Hall system valid near simple rational numbers of magnetic flux quanta per…
The electronic structure of bilayer graphene under pressure develops very interesting features with an enhancement of the trigonal warping and a splitting of the parabolic touching bands at the K point of the reciprocal space into four…
We present a symmetry-based analysis of competition between different gapped states that have been proposed in bilayer graphene (BLG), which are all degenerate on a mean field level. We classify the states in terms of a hidden SU(4)…
We theoretically investigate the effect of an attractive on-site interaction on the two-band magnetic Dirac fermion model based on a square lattice system. When the attractive fermion interaction is taken into account by the mean-field…
In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions…
We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows…
Graphene enables precise carrier-density control via gating, making it an ideal platform for studying electronic interactions. However, sample inhomogeneities often limit access to the low-density regimes where these interactions dominate.…
Starting from the Hamiltonian operator of the noncompensated two-sublattice model of a small antiferromagnetic particle, we derive the effective Lagrangian of a biaxial antiferromagnetic particle in an external magnetic field with the help…
We theoretically study the quantum Hall effect (QHE) in graphene with an ac electric field. Based on the tight-binding model, the structure of the half-integer Hall plateaus at $\sigma_{xy} = \pm(n + 1/2)4e^2/h$ ($n$ is an integer) gets…
We compute the energy spectrum of a nearest-neighbor electron hopping model for bi-layer graphene at commensurate twist angles. Specifically, we focus on the simplest bi-layer lattices, with moire patterns that have no subcells. The…
The physics of the fractional quantum Hall effect is the physics of interacting electrons confined to a macroscopically degenerate Landau level. In this Chapter we discuss the theory of the quantum Hall effect in systems where the electrons…
"Photonic crystals" built with time-reversal-symmetry-breaking Faraday-effect media can exhibit "chiral" edge modes that propagate unidirectionally along boundaries across which the Faraday axis reverses. These modes are precise analogs of…
There is no assurance that interface states can be found at the boundary separating two materials. As a strong perturbation typically favors wave localization, it is natural to expect that an interface state should form more easily in the…
Studies of twisted moir\'e systems have been mainly focused on two-dimensional (2D) materials such as graphene with Dirac points and transition-metal-dichalcogenide so far. Here we propose a twisted bilayer of 2D systems which feature…
Quantum Hall effect in 1,2-layer graphene is analyzed. The transverse and longitudinal resistivity are found to be universal functions of the filling factor and temperature. At fixed magnetic field mode the magneto-transport problem is…
The spin Hall effect of light, a spin-dependent transverse splitting of light at an optical interface, is intrinsically an incident-polarization-sensitive phenomenon. Recently, an approach to eliminate the polarization dependence by…