Quantum Hall Effect at Finite Temperatures

text of abstract (Integer quantum Hall effect (IQHE) has been analysed considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted and their variation is studied as a function of magnetic field. The number of current carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis attempts to answer certain basic questions besides providing a simple but complete understanding of IQHE.)

We study the Landau level localization and scaling properties of a disordered two-dimensional electron gas in the presence of a strong external magnetic field. The impurities are treated as random distributed scattering centers with parameterized potentials. Using a transfer matrix for a finite-width strip geometry, we calculate the localization length as a function of system size and electron energy. The finite-size localization length is determined by calculating the Lyapun...

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 classification, and a criterion for the validity of the mean-field approximation in the charge-density-wave phase, is based on scaling arguments concerning the effective interaction potential of electrons restricted to an arbitrary Landau level. Finite-...

This paper is a lab tutorial (and a theory primer) for the integral quantum Hall effect experiment as conducted at Applied Solid State Physics, University of Bochum, Germany.

It is widely held that disorder is essential to the existence of a finite interval of magnetic field in which the Hall conductance is quantized, i.e. for the existence of `plateaus' in the quantum Hall effect. Here, we show that the existence of a quasi-particle Wigner crystal results in the persistence of plateaus of finite extent even in the limit of vanishing disorder. Several experimentally detectable features that characterize the behavior in the zero disorder limit are ...

We investigate the energy exchanges along an electronic quantum channel realized in the integer quantum Hall regime at filling factor $\nu_L=2$. One of the two edge channels is driven out-of-equilibrium and the resulting electronic energy distribution is measured in the outer channel, after several propagation lengths $0.8~\mu$m$\leq L\leq30~\mu$m. Whereas there are no discernable energy transfers toward thermalized states, we find efficient energy redistribution between the ...

Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all physical properties are dictated solely by many-body effects. A remarkable consequence is the emergence of new quasiparticles with fractional charge and exotic quantum statistics of which the most exciting ones are non-Abelian quasiparticles...

This lecture note reviews a variety of transport and thermodynamic measurements of electron decoherence time in low-dimensional conductors at low temperature. The mechanism of dephasing by electron interaction mediated by an arbitrarily small number of magnetic impurities is neither applicable to our linear-response measurements of weak localization, nor is it observed in the recent high-field measurements of the decoherence time in nominally pure quasi-one dimensional gold w...

We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $-0.66\pm0.04$. Thus the non-interacting fixed point (characterized $z=2$ and $\nu\approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ($z=1$, $\nu\ap...

Electron drag between two two-dimensional electron gases in magnetic fields has been observed with a polarity opposite that for zero field. This negative drag requires that the electrons have a hole-like dispersion. Density dependence measurements in the integer quantum Hall regime show that drag is negative only when the upper Landau level of one layer is more than half filled while the other is less than half filled, indicating that hole-like dispersion is present in a half...