Related papers: Towards the fractional quantum Hall effect: a nonc…
We clearly show that the symplectic structures deformations lead, upon quantization, to quantum theories of non commutative fields. Two variants of deformations are considered. The quantization is performed and the modes expansions of the…
We discuss quantum Hall effect in the presence of arbitrary pair interactions between electrons. It is shown that irrespective of the interaction strength the Hall conductivity is given by the filling fraction of Landau levels averaged over…
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the electron spin or the density, as decided by the details of…
It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed…
In this contribution, we present an introduction to the physical principles underlying the quantum Hall effect. The field theoretic approach to the integral and fractional effect is sketched, with some emphasis on the mechanism of…
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 show that our recently proposed method\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural connection with the geometry of the fractional…
Quantum geometric electronic responses are often viewed through a non-interacting lens: independent quasiparticles accumulate Berry phases as they move through a static crystal and background potential. Here we argue that the combined…
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 investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body…
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…
It is demonstrated that all observed fractions at moderate Landau level fillings for the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility to have the special…
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…
We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer…
The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may…
The quantum anomalous Hall effect refers to the quantization of Hall effect in the absence of applied magnetic field. The quantum anomalous Hall effect is of topological nature and well suited for field-free resistance metrology and…
Area non-preserving transformations in the non-commutative plane are introduced with the aim to map the $\nu=1$ integer quantum Hall effect (IQHE) state on the fractional quantum Hall effect (FQHE) $\nu=\frac{1}{2p+1}$ FQHE states. Using…
With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some…
We study quantum Hall effect within the framework of a newly proposed approach, which captures the principal results of some proposals. This can be established by considering a system of particles living on the non-commutative plane in 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…