Related papers: Phase Diagram of Integer Quantum Hall Effect
The quantized Hall conductance in a plateau is related to the index of a Fredholm operator. In this paper we describe the generic ``phase diagram'' of Fredholm indices associated with bounded and Toeplitz operators. We discuss the possible…
We study transport properties and topological phase transition in two-dimensional interacting disordered systems. Within dynamical mean-field theory, we derive the Hall conductance, which is quantized and serves as a topological invariant…
We study numerically conductance fluctuations near the integer quantum Hall effect plateau transition. The system is presumed to be in a mesoscopic regime, with phase coherence length comparable to the system size. We focus on a…
We summarize the screening theory of the integer quantized Hall effect (IQHE) and emphasize its two key mechanisms: first, the existence, in certain magnetic field intervals, of incompressible strips, with integer values of the local…
The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities…
We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate Landau levels, Zeeman splitting and level crossings in the presence of changing…
By numerical exact diagonalization techniques, we obtain the quantum phase diagram of the lattice fractional quantum Hall (FQH) systems in the presence of quenched disorder. By implementing an array of local potential traps representing the…
We derive an empirical formula for the width of quantum Hall effect plateaus which is free of adjustable parameters. It describes the integer, fractional and $\nu = 0$ (Wigner insulator) quantum Hall effect in single heterojunctions. The…
We present a new theoretical approach for the integer quantum Hall effect, which is able to describe the inter-plateau transitions as well as the transition to the Hall insulator. We find two regimes (metallic and insulator like) of the top…
The conductivity $\sigma$ and resistivity $\rho$ tensors of the disordered Hofstadter model are mapped as functions of Fermi energy $E_F$ and temperature $T$ in the quantum critical regime of the plateau-insulator transition (PIT). The…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
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…
We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the…
Quantum Hall effect (QHE), the ground to construct modern conceptual electronic systems with emerging physics, is often much influenced by the interplay between the host two-dimensional electron gases and the substrate, sometimes predicted…
After decades of searching for the dissipationless transport in the absence of any external magnetic field, quantum anomalous Hall effect (QAHE) was recently achieved in magnetic topological insulator (TI) films. However, the universal…
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…
We study quantum phase transitions involving fractional quantum Hall states, using numerical calculations of entanglements and related quantities. We tune finite-size wavefunctions on spherical geometries, by varying the interaction…
We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple…
A two-dimensional lattice model for non-interacting fermions in a magnetic field with half a flux quantum per plaquette and $N$ levels per site is considered. This is a model which exhibits the Integer Quantum Hall Effect (IQHE) in the…