Related papers: The Eight Dimensional Quantum Hall Effect and the …
The geometrical application of split octonions is considered. The modified Fano graphic, which represents products of the basis units of split octonionic, having David's Star shape, is presented. It is shown that active and passive…
In Quantum Hall effect the ground state wave function at $\nu=1$ is the building block of all other states at different filling factors. It is developed by the entanglement of two spinors forming a singlet state. The inherent frustration…
Until the late 1980s, phases of matter were understood in terms of Landau's symmetry breaking theory. Following the discovery of the quantum Hall effect the introduction of a second class of phases, those with topological order, was…
We show that in the limit of zero temperature, double layer quantum Hall systems exhibit a novel phenomena called Hall drag, namely a current driven in one layer induces a voltage drop in the other layer, in the direction perpendicular to…
We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the…
The fractional quantum Hall effect was experimentally discovered in 1982. It was observed that the Hall conductivity $\sigma_{yx}$ of a two-dimensional electron system is quantized, $\sigma_{yx}=e^2/3h$, in the vicinity of the Landau level…
A scanning probe technique was used to obtain a high-resolution map of the random electrostatic potential inside the quantum Hall liquid. A sharp metal tip, scanned above a semiconductor surface, sensed charges in an embedded…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…
Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field $\mathbf{g}(x)$ influences the QHE. In the…
We discuss the ordinary quantum Hall effect and a higher-dimensional cousin. We consider the dimensional reduction of these effects to 1+1 and 3+1 space-time dimensions, respectively. After dimensional reduction, an axion field appears,…
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 report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…
Topology establishes a unifying framework for a diverse range of scientific areas including particle physics, cosmology, and condensed matter physics. One of the most fascinating manifestations of topology in the context of condensed matter…
The temperature driven flow lines of the Hall and dissipative magnetoconductance data (\sigma_{xy},\sigma_{xx}) are studied in the fractional quantum Hall regime for a 2D electron system in GaAs/Al_{x}Ga_{1-x}As heterostructures. The flow…
We propose two non-abelian Chern-Simons matrix models as the effective descriptions of 4-dimensional quantum Hall fluids. One of them describes a new type of 4-dimensional quantum Hall fluid on the space of quaternions, the other provides…
The unusual properties of two-dimensional electron systems that give rise to the quantum Hall effect have prompted the development of new microscopic models for electrical conduction. The bulk properties of the quantum Hall effect have also…
This is a pedagogical exposition of holonomy groups intended for physicists. After some pertinent definitions, we focus on special holonomy manifolds, two per division algebras, and comment upon several cases of interest in physics,…
A formalism is presented for treating strongly-correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle--hole generators. The graphene SO(8) algebra is isomorphic to…
We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…
We report magneto-transport studies of a two-dimensional electron system formed in an inversion layer at the interface between a hydrogen-passivated Si(111) surface and vacuum. Measurements in the integer quantum Hall regime demonstrate the…