Related papers: Quantum Hall effect at low magnetic fields
Recent developments in the scaling theory of the integer quantum Hall effect are discussed. In particular, the influence of electron-electron interactions on the critical behavior are studied. It is further argued that recent experiments on…
The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are…
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…
We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to…
The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and…
The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of $e^2/h$. Here we show that the…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…
We have studied the conductivity peak in the transition region between the two lowest integer Quantum Hall states using transmission measurements of edge magnetoplasmons. The width of the transition region is found to increase linearly with…
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…
The fate of integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of {\it correlated} disorders. We find a systematic {\it float-up} and {\it merging} picture for extended levels on the low-energy…
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak…
Low frequency AC-measurements are commonly used to determine the voltage and currents through mesoscopic devices. We calculate the effect of the alternating Hall voltage on the recorded time-averaged voltage in the presence of a top-gate…
A numerical analysis is made of the breakdown of the quantum Hall effect caused by the Hall electric field in competition with disorder. It turns out that in the regime of dense impurities, in particular, the number of localized states…
I review some aspects of an alternative model of the quantum Hall effect, which is not based on the presence of disorder potentials. Instead, a quantization of the electronic drift current in the presence of crossed electric and magnetic…
We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical…
As a model for the transitions between plateaus in the fractional Quantum Hall effect we study the critical behavior of non-interacting charged particles in a static random magnetic field with finite mean value. We argue that this model…
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…
We present a simple classification of the different liquid and solid phases of quantum Hall systems in the limit where the Coulomb interaction between the electrons is significant, i.e. away from integral filling factors. This…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
We report results of numerical studies of the integer quantum Hall effect in a tight binding model on a two-dimensional square lattice with non-interacting electrons, in the presence of a random potential as well as a uniform magnetic field…