Quantum Hall Effect at Finite Temperatures

In the strong magnetic field fractional quantum Hall regime, electrons in a two-dimensional electron system are confined to their lowest Landau level. Because of the macroscopic Landau level degeneracy nearly all physical properties at low energies and temperatures are then entirely determined by electron-electron interactions. The properties of these non-Fermi-liquid electronic systems continue to surprise. In this article we briefly survey some recent advances in the physic...

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the electronic transport properties due to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder...

The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical results for the influences of interaction and disorder on the compressibility as a function of the particle density and the strength of the magnetic field are presented. Localization-delocalization transitions associated with highly compres...

We argue that the finite temperature dynamics of the integer quantum Hall system is governed by two independent length scales. The consistent scaling description of the transition makes crucial use of two temperature critical exponents, reflecting the interplay between charging effects and interaction-induced dephasing. Experimental implications of the two-scale picture are discussed.

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 of non-interacting electrons are considered in detail. Results for the frequency scaling at the critical point and for the frequency dependent deviation of the Hall conductivity from the quantised plateau value are presented.

The present theory has investigated the FQHE without any quasi-particle. The electric field due to the Hall voltage is taken into consideration. We find the ground state where the electron configuration is uniquely determined so as to have the minimum classical Coulomb energy. Residual Coulomb interaction HI yields quantum transitions which satisfy the momentum conservation along the current direction. The number of Coulomb transitions from nearest electron pairs is dependent...

We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find numerical evidence for dynamical scaling with a dynamical critical exponent z=1 at the integer quantum Hall plateau transition in the lowest Landau level. Within the numerical accuracy of our data the conductivity at the transition and the anomal...

Experimental studies of the transitions from a primary quantum Hall (QH) liquid at filling factor 1/k (with k an odd integer) to the insulator have indicated a ``quantized Hall insulator'' (QHI) behavior: while the longitudinal resistivity diverges with decreasing temperature and current bias, the Hall resistivity remains quantized at the value $k h/ e^2$. We review the experimental results and the theoretical studies addressing this phenomenon. In particular, we discuss a th...

We study effects of disorder on the integer quantized Hall effect within the screening theory, systematically. The disorder potential is analyzed considering the range of the potential fluctuations. Short range part of the single impurity potential is used to define the conductivity tensor elements within the self-consistent Born approximation, whereas the long range part is treated self-consistently at the Hartree level. Using the simple, however, fundamental Thomas-Fermi sc...

We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energ...