Global phase diagram in the quantum Hall effect

Levitation of current carrying states in the lattice model for the integer quantum Hall effect

The disorder driven quantum Hall to insulator transition is investigated for a two-dimensional lattice model. The Hall conductivity and the localization length are calculated numerically near the transition. For uncorrelated and weakly correlated disorder potentials the current carrying states are annihilated by the negative Chern states originating from the band center. In the presence of correlated disorder potentials with correlation length larger than approximately half the lattice constant the floating up of the critical states in energy without merging is observed. This behavior is similar to the levitation scenario proposed for the continuum model.

Bilayer coherent and quantum Hall phases: duality and quantum disorder

We consider a fully spin-polarized quantum Hall system with no interlayer tunneling at total filling factor nu = 1/k (where k is an odd integer) using the Chern-Simons-Ginzburg-Landau theory. Exploiting particle-vortex duality and the concept of quantum disordering, we find a large number of possible compressible and incompressible ground states, some of which may have relevance to recent experiments of Spielman et al. [Phys. Rev. Lett. 84, 5808 (2000)]. We find interlayer coherent compressible states without Hall quantization and interlayer incoherent incompressible states with Hall quantization in addition to the usual (k,k,k) Halperin states, which are both interlayer coherent and incompressible.

Quantum hall effect at low magnetic fields

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 Landau quantization becomes dominant.

Probing the plateau-insulator quantum phase transition in the quantum hall regime

We report quantum Hall experiments on the plateau-insulator transition in a low mobility In(0.53)Ga(0.47)As/InP heterostructure. The data for the longitudinal resistance rho(xx) follow an exponential law and we extract a critical exponent kappa = 0.55+/-0. 05 which is slightly different from the established value kappa = 0. 42+/-0.04 for the plateau transitions. Upon correction for inhomogeneity effects, which cause the critical conductance sigma(*)(xx) to depend marginally on temperature, our data indicate that the plateau-plateau and plateau-insulator transitions are in the same universality class.