Related papers: Comments on the Chern Number Argument of the Integ…
The quantum anomalous Hall system with Chern number 2 can be destroyed by sufficiently strong disorder. During its process towards localization, it was found that the electronic states will be directly localized to an Anderson insulator…
The The composite fermion model (CF) of the quantum Hall effect which gives the correct series of charges is based on attachment of flux quanta to the electron. The construction of the series of charges leads to a field expression which…
We study the phase diagram of interacting electrons in a dispersionless Chern band as a function of their filling. We find hierarchy multiplets of incompressible states at fillings \nu=1/3, 2/5, 3/7, 4/9, 5/9, 4/7, 3/5 as well as…
The quantum Hall system is known to have two mutually dual Chern-Simons descriptions, one associated with the hydrodynamics of the electron fluid, and another associated with the statistics. Recently, Susskind has made the claim that the…
We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density.…
We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\delta$-function potentials arranged in different geometric configurations. When the number of delta functions…
We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wavefunctions, compute the drift and…
We study the finite temperature (FT) effects on integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) as predicted by the composite fermion model. We find that at $T\neq 0$, universality is lost, as is quantization…
Motivated by the successful idea of using weakly-coupled quantum electronic wires to realize the quantum Hall effects and the quantum spin Hall effects, we theoretically construct two systems composed of weakly-coupled quantum spin chains,…
There are compelling reasons to seek a new coherent description of the Quantum Hall Effects (QHE). The theories of the `Integer' (IQHE) and the `Fractional' (FQHE) quantum Hall effects are very different at present, despite their remarkable…
In a recent paper by Neupert, Santos, Chamon, and Mudry [Phys. Rev. B 86, 165133 (2012)] it is claimed that there is an elementary formula for the Hall conductivity of fractional Chern insulators. We show that the proposed formula cannot…
We propose a (4+1) dimensional Chern-Simons field theoretical description of the fractional quantum Hall effect. It suggests that composite fermions reside on a momentum manifold with a nonzero Chern number. Based on derivations from…
It is often stated that complex numbers are essential in quantum theory. In this article, the need for complex numbers in quantum theory is motivated using the results of tandem Stern-Gerlach experiments
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…
It is shown that the statements about the observation of the transitions between the insulating phase and the integer quantum Hall effect phases with the quantized Hall conductivity $\sigma_{xy}^{q}$ $\geq 3e^{2}/h$ made in a number of…
We begin by explaining how a physical problem of studying the quantum Hall effect on a closed surface $C$ leads, via Laughlin's approach, to a mathematical question of describing the rank and the first Chern class of a particular vector…
We present a pedagogical review of the physics of fractional Chern insulators with a particular focus on the connection to the fractional quantum Hall effect. While the latter conventionally arises in semiconductor heterostructures at low…
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…
Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome.…
Theoretical developments during the past several years have shown that large scale properties of the Quantum Hall system can be successfully described by effective field theories which use the Chern-Simons interaction. In this article, we…