Related papers: Quantum Hall Dynamics on von Neumann Lattice
We study how the stability of the fractional quantum Hall effect (FQHE) is influenced by the geometry of band structure in lattice Chern insulators. We consider the Hofstadter model, which converges to continuum Landau levels in the limit…
We show that the Fractional Quantum Hall Effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid. This flow consists of a large number of vortices of the same chirality. In this approach each…
Applying a unified approach, we study integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) in the Hofstadter model with short range interaction between fermions. An effective field, that takes into account the…
The recent Quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice,…
We propose that Hofstadter's butterfly accompanied by quantum Hall effect that is similar to those predicted to occur in 3D tight-binding systems by Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized in an…
Thermodynamic and electric properties of anisotropic compressible Hall states at higher Landau levels are studied using a mean field theory on the von Neumann lattice basis. It is shown that resistances agree with the recent experiments of…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…
The low-lying excitations of a quantum Hall state on a disk geometry are edge excitations. Their dynamics is governed by a conformal field theory on the cylinder defined by the disk boundary and the time variable. We give a simple and…
The quantization of Hall conductance in a p-type heterojunction with lateral surface quantum dot superlattice is investigated. The topological properties of the four-component hole wavefunction are studied both in r- and k-spaces. New…
We discuss the relationship between the quantum Hall conductance and a fractal energy band structure, Hofstadter's butterfly, on a square lattice under a magnetic field. At first, we calculate the Hall conductance of Hofstadter's butterfly…
We derive effective Hamiltonians for the fractional quantum Hall effect in n=0 and n=1 Landau levels that account perturbatively for Landau level mixing by electron-electron interactions. To second order in the ratio of electron-electron…
A two-dimensional array of quantum dots in a magnetic field is considered. The electrons in the quantum dots are described as unitary random matrix ensembles. The strength of the magnetic field is such that there is half a flux quantum per…
A fractional quantization in a two dimensional space is proposed. The angular momenta of the two dimensional electrons are quantized in fractional numbers by the boundary conditions on a multi-layered Riemann surface. Extended wave…
We derive the condition for the occurrence of the integer quantum Hall effect in two-dimensional lattice systems with interactions, expressed as $\phi\nu-\rho\in\mathbb{Z}$, where $\phi$, $\nu$, and $\rho$ denote the magnetic flux, the…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
Recently unusual integer quantum Hall effect was observed in graphene in which the Hall conductivity is quantized as $\sigma_{xy}=(\pm 2, \pm 6, \pm 10, >...) \times \frac{e^2}{h}$, where $e$ is the electron charge and $h$ is the Planck…
We introduce and study the Wannier functions for an electron moving in a plane under the influence of a perpendicular uniform and constant magnetic field. The relevance for the Fractional Quantum Hall Effect is discussed; in particular it…
We address two fundamental issues in the physics of the quantum Hall effect: a unified description of scaling behavior of conductances in the integral and fractional regimes, and a quasi-particle formulation of the chiral Luttinger Liquids…
The quantum Hall effect was originally observed in a two-dimensional electron gas forming Landau levels when exposed to a strong perpendicular magnetic field and was later generalized to Chern insulators without net magnetization. Here,…
Considering lattice Hamiltonians designed using conformal field theory to have fractional quantum Hall states as ground states, we study the dynamics of one or two particles on such lattices. Examining the eigenspectrum and dynamics of the…