Universal scaling results for the plateau–insulator transition in the quantum Hall regime

Abstract

We report new experimental data on the plateau-insulator transition in the quantum Hall regime, taken from a low mobility InGaAs/InP heterostructure. By employing the fundamental symmetries of the quantum transport problem we are able to disentangle the universal quantum critical aspects of the magnetoresistance data (critical indices and scaling functions) and the sample dependent aspects due to macroscopic inhomogeneities. Our new results and methodology indicate that the previously established experimental value for the critical index (κ = 0.42) resulted from an admixture of both universal and sample dependent behavior. A novel, non-Fermi liquid value is found (κ = 0.57) along with the leading corrections to scaling. The statement of self-duality under the Chern Simons flux attachment transformation is verified.PACS numbers: 73.20.Dx, 73.40.Hm More than ten years ago, H.P.Wei et al.[1] demonstrated experimentally that the plateau transitions in the quantum Hall regime display all the features of a conventional, disorder induced metal-insulator transition [2]. The transport data, taken from low mobility InGaAs/InP heterostructures at low temperatures T , were shown to depend on the single scaling variable T −κ ∆ν only. Here, ∆ν represents the filling fraction of the Landau band ν relative to the critical value ν c ≈ half-integer. The quantity of central physical interest is the exponent κ. This represents the ratio of two independent critical indices κ = p/2ν. Here, the exponent p, originally identified as the inelastic scattering time exponent, determines the relation between the phase breaking length l φ and temperature T according to l φ ∝ T −p/2 . Theν is the exponent of the correlation length ξ that diverges at the Landau band center according to ξ = |∆ν| −ν . The quoted best experimental value for κ is given by κ ≈ 0.42 [1,3].However, even currently the precise meaning of the exponent κ and the very nature of the quantum critical phase remain a major topic of both experimental and theoretical research. From the theoretical side, a microscopic theory for localization and Coulomb interaction effects has been developed only recently [4,5,6]. The theory now shows that the physical observable, associated with the exponent p, is none other than the specific heat of the electron gas c v ∝ T p . From the experimental point of view, there are still major complications in approaching the true T = 0 asymptotics of scaling. One of the main difficulties in probing quantum criticality in the quantum Hall regime is that the experiment must be performed on samples where the scattering is mainly provided by short-ranged potential fluctuations. Slowly varying potential fluctuations, like those present in the GaAs/AlGaAs heterostructure, give rise to cross-over effects that dramatically complicate the observability of quantum criticality in the quantum Hall regime [4].The effect of macroscopic sample inhomogeneities, which are inherent to the experiments, on the critical behavior of the plateau transitions is still not...

Super Universality of the Quantum Hall Effect and the “Large N Picture” of the ϑ Angle

“…Hall plateau transitions are essentially the same as those taken from the free electron gas [27] and observed in the experiment [28][29][30][31].…”

“…We mention, in particular, the Finkelstein approach to localization and interaction effects [21,22] which explains why the infinitely ranged Coulomb interaction does not affect the basic phenomena of scaling as predicted by the free electron gas [27] and observed in the experiment [28][29][30][31]. The Finkelstein approach, however, fundamentally alters our understanding of the quantum critical behavior of the electron gas.…”

Emergence of integer quantum Hall effect from chaos

“…(Recall that the longitudinal conductivity in the present work, defined based on the effective field theory, differs from that in conventional IQHE by a factor of 2.) They are in good agreement with the data for conventional IQHE systems 71,[74][75][76][77] . Note that because finite-time effects are enhanced by increasing h The effective field theory (65) holds only forω incommensurate with 2π.…”

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).…”