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Among the various geometries to study the fractional quantum Hall effect in two dimensional electron gas, the Corbino disc owns the advantage to probe the bulk properties directly. In this work we explore the influence of in-plane electric…
We perform variational Monte-Carlo calculations to show that bosons in a rotating optical lattice will form analogs of fractional quantum Hall states when the tunneling is sufficiently weak compared to the interactions and the deviation of…
We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism…
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects…
Generalizing from previous work on the integer quantum Hall effect, we construct the effective action for the analog of Laughlin states for the fractional quantum Hall effect in higher dimensions. The formalism is a generalization of the…
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
The fractional quantum Hall effect (FQHE) is theoretically investigated, with numerical and algebraic approaches, in assemblies of a few spinful ultracold neutral fermionic atoms, interacting via repulsive contact potentials and confined in…
The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb…
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…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
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…
In the fractional quantum Hall effect regime we measure diagonal ($\rho_{xx}$) and Hall ($\rho_{xy}$) magnetoresistivity tensor components of two-dimensional electron system (2DES) in gated GaAs/Al$_{x}$Ga$_{1-x}$As heterojunctions,…
Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor $\nu=1/2$ as we tilt the sample in the magnetic field. Starting with a…
In two space dimensions the possibilities of fractional spin as well as fractional statistics exist. I examine the relation between fractional spin and statistics for Laughlin quasi-particles in a two-dimensional electron system with…
The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the…
This lecture aims to present an overview of the properties of Hall effect devices. Descriptions of the Hall phenomenon, a review of the Hall effect device characteristics and of the various types of probes are presented. Particular…
This article reviews the development of photonic analogues of quantum Hall effects, which have given rise to broad interest in topological phenomena in photonic systems over the past decade. We cover early investigations of geometric…
We consider the behaviour of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low energy, large system limit. Using the close links between quantum Hall wavefunctions and conformal field theories we construct…
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the…