Related papers: Arithmetic of the integer quantum Hall effect
We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…
We consider recent experimental results [W. Pan {\it et al}, Phys. Rev. Lett. {\bf 90}, 016801 (2003)] for occurrence of the fractional quantum Hall effect-FQHE under the perspective of our formulation in terms of {\it fractons}. These…
In a recent Rapid Communication ``Observation of the $\nu=1$ quantum Hall effect in a strongly localized two-dimensional system,'' Shahar, Tsui, and Cunningham reported a disorder --- magnetic field phase diagram for the integer quantum…
The integer quantum Hall effect (QHE) belongs to the most fundamental phenomena of solid state physics and has an important application as resistance standard. It serves as a basis to understand the fractional, anomalous or spin QHEs,…
We investigate the theory of the fractional quantum Hall effect (QHE) proposed a long time ago by Lopez and Fradkin \cite{Fradkin1991chern} to describe the principal Jain series. The magnetic fluxes of the statistical gauge field attached…
The quantum anomalous Hall effect (QAHE) realizes dissipationless longitudinal resistivity and quantized Hall resistance without the need of an external magnetic field. However, when reducing the device dimensions or increasing the current…
The classical Hall effect in inhomogeneous systems is considered for the case of one-dimensional inhomogeneity. For a certain geometry of the problem and for the magnetic field linearly depending on the coordinate the density of current…
We develop a simple kinetic equation description of edge state dynamics in the fractional quantum Hall effect (FQHE), which allows us to examine in detail equilibration processes between multiple edge modes. As in the integer quantum Hall…
Our microscopic understanding of the integer quantum Hall effect is still incomplete. For decades, there has been a controversial discussion about "where the current flows" if the Hall resistance is quantized. Here, we qualitatively analyze…
This is an introduction to the microscopic theories of the FQHE. After a brief description of experiments, trial wavefunctions and the physics they contain are discussed. This is followed by a description of the hamiltonian approach,…
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…
Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separatly, this problem is equivalent to that of a one…
Quantum dots in the quantum Hall regime can have pairs of single Slater determinant states that are degenerate in energy. We argue that these pairs of many body states may give rise to a Kondo effect which can be mapped into an ordinary…
We have studied the fractional and integer quantum Hall (QH) effects in a high-mobility double-layer two-dimensional electron system. We have compared the "stability" of the QH state in balanced and unbalanced double quantum wells. The…
The integer quantum Hall effect (QHE) and one-dimensional Anderson localization (AL) are limiting special cases of a more general phenomenon, directed localization (DL), predicted to occur in disordered one-dimensional wave guides called…
The integer quantum Hall transition (IQHT) is one of the most mysterious members of the family of Anderson transitions. Since the 1980s, the scaling behavior near the IQHT has been vigorously studied in experiments and numerical…
Many computationally hard problems can be encoded in quantum Hamiltonians. The solution to these problems is given by the ground states of these Hamiltonians. A state-of-the-art algorithm for finding the ground state of a Hamiltonian is the…
The angular momentum of the Hall particles acquiring Berry phases from quantization,is the very source of unifying the physics of IQHE and FQHE. The origin of {\it Shift} quantum number lies in the change of angular momentum of the Hall…
We analyze the recently observed breakdown of the integer quantum Hall effect in a two-dimensional electron gas embedded in a metallic split-ring resonator. By accounting for both the quantized vacuum field and electrostatic boundary…
We consider a recently proposed network model of the integer quantum Hall (IQH) effect in a weak magnetic field. Using a supersymmetry approach, we reformulate the network model in terms of a superspin ladder. A subsequent analysis of the…