A new transport regime in the quantum Hall effect

Abstract

Our evolving understanding of the dramatic features of charge-transport in the quantum Hall (QH) regime has its roots in the more general problem of the metal-insulator transition. Conversely, the set of conductivity transitions observed in the QH regime provides a fertile experimental ground for studying many aspects of the metal-insulator transition. While earlier works [1,2] tend to concentrate on transitions between adjacent QH liquid states, more recent works [3-8] focus on the transition from the last QH state to the high-magnetic-field insulator. Here we report on measurements that identified a novel transport regime which is distinct from both, the fully developed QH liquid, and the critical scaling regime believed to exist asymptotically close to the transition at very low temperatures (T 's).This new regime appears to hold in a wide variety of samples and over a large range of magnetic field (B) and temperature. It is characterized by a remarkably simple phenomenological scaling of the longitudinal resistivity (ρ xx ), which is the center of this letter, and is not understood theoretically.We begin by focusing on a recent set of observations that directly begot some of the results presented here. In Refs. [9,10], the observation of a new symmetry was reported, relating the transport properties of the QH liquid to those of the adjacent insulator. For the case of the ν = 1 to insulator transition, this symmetry is summarized by:where ν is the Landau level filling factor, ∆ν = ν −ν c and ν c is the critical ν of the transition (see the inset of Fig. 1 for the identification of ν c ). Remarkably, a similar symmetry holds at transitions from the 1/3 fractional quantum Hall (FQH) state to the insulator, if one replaces the ν's in Eq. 1 with those of composite fermions [11]. In addition, in ref.[9] we showed that a generalized relation holds, within experimental error, even for the non-linear regime of transport, and suggested the possibility that duality symmetry underlies this relation [9,12]. More recently, a similar relation was observed in Si-MOSFET samples near the B = 0 conductor-insulator transition [13], which raises the question whether a more general explanation may exist for the symmetry [14].In the remainder of this paper we shall present and discuss a view of the ρ xx data where the symmetry of Eq. 1 is a straightforward ingredient. We begin by plotting, in Fig. 1, ρ xx vs. ν for a low mobility (µ = 30000 cm 2 /Vsec), low density (n = 3 · 10 10 cm −2 ), InGaAs/InP sample, in the range of 0.4 < ν < 0.8 which includes the ν = 1-to-insulator transition (ν = 0.562), at several T 's between 0.072 and 2.21 K. Rather than plotting the data using the conventional linear ordinate (see inset of Fig. 1), we chose a log scale, which clearly reveals a distinct ν dependence of ρ xx :where ρ xx is measured in units of its critical value, ρ xxc (= 29.6 kΩ for this sample), a normalization which we adopt throughout this letter, and ν 0 (T ) is a T -dependent logarithmic slope, introduced here for the first time....

Quantum Fluctuations and the Closing of the Coulomb Gap in a Correlated Insulator

“…Quantitative analysis closer to the MI transition will require lower temperature experiments in order to continue to capture the interplay of the Coulomb gap and quantum fluctuation physics. We note, that unlike the phenomenology near the quantum Hall-to-insulator transition [19], scaling here remains critical. The ability to treat the insulator on an equal footing with the metal Carrier density n for each data set is indicated in the legend in units of 10 19 cm ÿ3 .…”

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).…”

Hopping Conductivity in the Quantum Hall Effect: Revival of Universal Scaling

“…Non-universal exponents were observed in the dependence of the transition width on temperature [15], current [16] and frequency [17]. Other experiments seem to contradict scaling theory at all, both for the Hall plateau-insulator transition [18] and the transition between QHE plateaus [19,20].However, before making conclusions on a general failure of scaling theory it has to be considered that nearly all experiments do not measure the localization length ξ directly. Therefore an assumption about the functional form and exponents z and p of the effective length L eff (T, I, f ) has to be made.…”

“…Non-universal exponents were observed in the dependence of the transition width on temperature [15], current [16] and frequency [17]. Other experiments seem to contradict scaling theory at all, both for the Hall plateau-insulator transition [18] and the transition between QHE plateaus [19,20].…”