Quantum Hall Effect at Finite Temperatures

The temperature and scale dependence of resistivities in the standard scaling theory of the integer quantum Hall effect is discussed. It is shown that recent experiments, claiming to observe a discrepancy with the global phase diagram of the quantum Hall effect, are in fact in agreement with the standard theory. The apparent low-field transition observed in the experiments is identified as a crossover due to weak localization and a strong reduction of the conductivity when La...

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F= < \delta g(E_F) \delta g(E_F + \Delta E) >$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the...

We consider Coulomb drag between two layers of two-dimensional electron gases subject to a strong magnetic field, with the Landau level filling factor in each layer being 1/2. We find $\rho_D$ to be very large, as compared to the zero magnetic field case. We attribute this enhancement to the slow decay of density fluctuations in a strong magnetic field. For a clean system, the linear $q$-dependence of the longitudinal conductivity, characteristic of the $\nu=1/2$ state, leads...

We have performed magnetotransport experiments in the high-temperature regime (up to 50 K) of the integer quantum Hall effect for two-dimensional electron gases in semiconducting heterostructures. While the magnetic field dependence of the classical Hall law presents no anomaly at high temperatures, we find a breakdown of the Drude-Lorentz law for the longitudinal conductance beyond a crossover magnetic field B_c ~ 1 T, which turns out to be correlated with the onset of the i...

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 Coulomb interaction on the scale of lattice constant. It is predicted that at a large in-plane component of the magnetic field such ordering will be present only at the filling factor |f|=1, and absent otherwise. Other experimental consequences o...

We have performed low-temperature transport measurements on a disordered two-dimensional electron system (2DES). Features of the strong localization leading to the quantum Hall effect are observed after the 2DES undergoes a direct insulator-quantum Hall transition with increasing the perpendicular magnetic field. However, such a transition does not correspond to the onset of strong localization. The temperature dependences of the Hall resistivity and Hall conductivity reveal ...

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 Hall effect that appeared to differ qualitatively from theoretical predictions as well as from experimental results obtained by others. In this Comment, I suggest a possible origin of this difference.

In order to obtain a local description of the short distance physics of fractionally quantized Hall states for realistic (e.g. Coulomb) interactions, I propose to view the zeros of the ground state wave function, as seen by an individual test electron from far away, as particles. I then present evidence in support of this interpretation, and argue that the electron effectively decomposes into quark-like constituent particles of fractional charge.

We study the finite temperature (FT) effects on integer quantum Hall effect (IQHE) and fractional quantum Hall effect (FQHE) as predicted by the composite fermion model. We find that at $T\neq 0$, universality is lost, as is quantization because of a new scale $T_0=\pi\rho /m^\ast p$. We find that this loss is not inconsistent with the experimentally observed accuracies. While the model seems to work very well for IQHE, it agrees with the bulk results of FQHE but is shown to ...

A breakdown of integer quantum Hall effect (IQHE) at strong disorder is studied numerically in a lattice model. We find a generic sequence by which the integer quantum Hall plateaus disappear: higher IQHE plateaus always vanish earlier than lower ones. We show that extended levels between these plateaus do not float up in energy but keep merging together after the disappearance of plateaus, which eventually leads to a localization in the whole system. We also study this pheno...