The quantum percolation model of the scaling theory of the quantum Hall effect: a unifying model for plateau-to-plateau transitions

Abstract

Abstract. We present a unifying model of plateau-to-plateau transitions in the quantum Hall effect based on results from high resolution frequency scaling experiments. We show that as the frequency or quantum coherence length of the two-dimensional electron system is varied, one observes a crossover between classical percolation and quantum percolation in the measured values of the critical scaling exponents of the plateau-to-plateau transitions. This crossover is dependent on the relationship between certain relevant length scales of a twodimensional system and can be explained using a quantum percolation model. The model explains why quantum criticality can be observed in some systems, but is absent from others.

A way of determination of axion mass with quantum Hall effect

“…We show that the axion effect can be observable in low temperature roughly below 100mK. According to our detailed analysis of the saturation, we find that critical frequency of saturation observed in previous experiment [37,38] strongly suggests axion mass ma = (0.95 ∼ 0.99) × 10 −5 eV.…”

“…Furthermore, similar scaling law holds when we imposed microwaves on Hall bar [33][34][35][36][37]. That is, ∆B ∝ f κ with κ = 0.4 ∼ 0.7 as the frequency f → 0 of the microwaves.…”

“…One is that f s does not depend on temperature and the other one is that f s does not depend on the size of Hall bar. Here we would like to point out that the previous experiment [37,38] using microwaves strongly suggests axion mass m a ≃ 0.95 × 10 −5 eV, because it seems that the critical frequency observed in the experiment satisfies two conditions presented in this paper.…”

“…The wave length 12cm ∼ 30cm is much larger than typical size of Hall bar. ) We will find later that axion mass m a = (0.95 ∼ 0.99) × 10 −5 eV, by analyzing a previous experiment [37,38] using microwaves imposed in quantum Hall effect. We explain in detail how the width ∆B depends on axion mass and temperature.…”

Phase transition and anomalous scaling in the quantum Hall transport of topological-insulator Sn−Bi1.1Sb0.9Xie1, Zhang2, Liu3 et al. 2019Phys. Rev. B

“…This discrepancy could be a result of various factors, including long-range disorder [7], spin-degenerate LLs [34], and macroscopic disorder [2], among others. For example, κ will increase from 0.42 towards 0.75 in conventional 2DEG when the disorder changes from short to long range [7], inducing a crossover from quantum to classical percolation with a change in γ from 7/3 to 4/3 [35]. None of these reasons explains our result, however, which is nearly half the universal value in conventional 2DEG.…”