Probing the Plateau-Insulator Quantum Phase Transition in the Quantum Hall Regime

Abstract

We report quantum Hall experiments on the plateau-insulator transition in a low mobility In.53Ga.47As/InP heterostructure. The data for the longitudinal resistance ρxx follow an exponential law and we extract a critical exponent κ = .55 ± .05 which is slightly different from the established value κ = .42±.04 for the plateau transitions. Upon correction for inhomogeneity effects, which cause the critical conductance σ * xx to depend marginally on temperature, our data indicate that the plateau-plateau and plateau-insulator transitions are in the same universality class.

Quantum criticality at the Chern-to-normal insulator transition

“…We compare these results with the known facts for the PIT in IQHE. 17,[19][20][21][22]24,[82][83][84][85] We find that, like at PIT in IQHE, the graphs of ρ xx as function of electron density, recorded at different temperatures, intersect at one single critical point, and they collapse into a single curve after a single-parameter rescaling. The scaling exponent κ is in good agreement with what one would predict by using the universally accepted value of the finite-size scaling exponent ν = 2.58 ± 0.03, 54,[86][87][88][89][90][91] and with p fixed like in our simulations (p = 1).…”

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

“…It was also speculated in Ref. 19 that this dependence most likely results from macroscopic inhomogeneities in the sample. In the latest papers [20][21][22] the frequency dependence of the QH transition width was studied.…”

“…The microscopic origin of these puddles was attributed to sample inhomogeneities. [16][17][18] (c) Very recent experimental results 19 on scaling of plateau-insulator as well as plateau-plateau QH transitions carried out on the same In x Ga 1−x As/InP sample as in Ref. 9 suggested that the narrowing of the transition width with temperature follows a power-law dependence ∆B ∝ T κ with κ ≈ 0.4.…”

“…Even when the authors of Ref. 19 analyzed their data using the procedure of Ref. 11, i.e., by plotting the logarithm of the longitudinal resistance versus ∆B, they obtained straight lines with slopes proportional to T κ ′ with κ ′ ≈ 0.55.…”

Possible existence of a band of extended states induced by inter-Landau-band mixing in a quantum Hall system

“…The integrally quantized Hall plateaus (IQHP) are observed when the Fermi level lies in localized states, with the value of the Hall conductance, σ xy = ne 2 /h, related to the number of occupied extended states(n). Many previous studies 3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23 have been focused on so-called plateau transitions. The issue there is how the Hall conductance jumps from one quantized value to another when the Fermi level crosses an extended state.…”