Related papers: Modular Groups, Visibility Diagram and Quantum Hal…

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…

It is demonstrated that all observed fractions at moderate Landau level fillings in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…

After more than three decades the fractional quantum Hall effect still poses challenges to contemporary physics. Recent experiments point toward a fractal scenario for the Hall resistivity as a function of the magnetic field. Here, we…

An effort is made to understand the phenomenological composite fermion model of the quantum Hall effect. The odd denominators are composed by adding plus minus 1 to the even numbers 2, 4, 6 and 8. Although the denominators are…

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu=N/(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the…

Using the path-integral formalism, we show that photons possess a nontrivial quantum metric in momentum space. We derive the semiclassical action and equations of motion by taking into account the quantum metric. In media with a spatially…

The fractional quantum Hall effect remains a captivating area in condensed matter physics, characterized by strongly correlated topological order, which manifests as fractionalized excitations and anyonic statistics. Numerical simulations,…

The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…

We report a simple route to generate magnetotransport data that results in fractional quantum Hall plateaus in the conductance. Ingredients to the generating model are conducting tiles with integer quantum Hall effect and metallic linkers,…

We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to…

We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…

Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…

We present a 6D generalization of the fractional quantum Hall effect involving membranes coupled to a three-form potential in the presence of a large background four-form flux. The low energy physics is governed by a bulk 7D topological…

We propose the existence and study the solitonic excitations in two kinds of samples in the fractional quantum Hall regime. One is a strip modulated by a one-dimensional array of gates. The other is made of two parallel strips coupled by a…

Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two…

Within the newly formulated composite fermion hierarchy the filling fraction of a spherical quantum Hall system is obtained when it can be expressed as an odd or even denominator fraction. A plot of $\nu\frac{2S}{N-1}$ as a function of $2S$…

We investigate low-temperature magneto-transport in recently developed, high-quality multi-terminal suspended bilayer graphene devices, enabling the independent measurement of the longitudinal and transverse resistance. We observe clear…

The Standard Model of particle physics stands as one of the most profound and successful frameworks for describing the fundamental workings of nature. The global form of the Standard Model gauge group, however, remains an open question: it…

These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…

The low energy neutral excitations of incompressible fractional quantum Hall states are called collective modes or magnetic excitons. This work develops techniques for computing their dispersion at general filling fractions for reasonably…