Fluctuating Hall resistance defeats the quantized Hall insulator

Abstract

Quantum Hall effects. PACS. 73.43.Nq -Quantum phase transitions. PACS. 64.60.Ak -Renormalization-group, fractal, and percolation studies of phase transitions (see also 61.43.Hv Fractals; macroscopic aggregates).Abstract. -Using the Chalker-Coddington network model as a drastically simplified, but universal model of integer quantum Hall physics, we investigate the plateau-to-insulator transition at strong magnetic field by means of a real-space renormalization approach. Our results suggest that for a fully quantum coherent situation, the quantized Hall insulator with RH ≈ h/e 2 is observed up to RL ∼ 25h/e 2 when studying the most probable value of the distribution function P (RH). Upon further increasing RL → ∞ the Hall insulator with diverging Hall resistance RH ∝ R κ L is seen. The crossover between these two regimes depends on the precise nature of the averaging procedure.Introduction. -The integer quantum Hall (QH) transitions are described well in terms of a series of delocalization-localization transitions of the electron wavefunction [1]. These universal plateau-plateau transitions are accompanied by a power-law divergence ǫ −ν of the electronic localization length ξ, where ǫ defines the distance to the transition for a suitable controlled parameter, e.g. the electron energy [2]. Similarly, it is now conclusively established that plateau-plateau and insulator-plateau transitions exhibit the same critical behavior [3][4][5][6].However, the value of the Hall resistance R H in this insulating phase (at large magnetic field) is still rather controversial. Various experiments have found that R H remains very close to its quantized value h/e 2 even deep in the insulating regime [4-6] with longitudinal resistance R L > h/e 2 . This scenario has been dubbed the quantized Hall insulator. On the other hand, theoretical predictions show that a diverging R H should be expected, i.e., R H ∝ R α L [7,8]. This Hall insulator is to be expected at strong disorder or strong magnetic fields.In fully quantum coherent transport measurements such as in mesoscopic devices at low temperature, the results clearly show the paramount influence of quantum interference and the measured quantities fluctuate strongly [9]. At magnetic field B = 0, the universal conductance fluctuations provide the most famous example [10]. For the QH situation, similarly reproducible and pronounced fluctuations have been observed previously [11][12][13][14], although no complete understanding of their behavior has yet emerged. Thus for quantum coherent QH

Observation of the quantized Hall insulator in the quantum critical regime of the two-dimensional electron gas

“…4 For this regime it is predicted that H ϳ 0 ␥ with ␥ ranging from 0.26-0.5. [4][5][6] This relation differs from our scaling result H ϳ 1+͑T͒ 0 which holds in the vicinity of the PI transition. Obviously, we did not mea-sure the magnetotransport properties to deep in the insulating phase.…”

“…3 The latter state has been named the "quantized Hall insulator." More recently, a breakdown of the quantized Hall insulator has been anticipated: [4][5][6][7] at large magnetic fields, deep in the insulating phase, the Hall resistivity diverges again when T → 0.…”

The Quantized Hall Insulator: A "Quantum" Signature of a "Classical" Transport Regime?

“…This regime of parameters is accessible; however, the main problem is that it is hard to obtain reliable experimental data deep in the insulating phase. In particular, due to the wide distribution of the Hall resistance, 31 its measured value is expected to be very sensitive to the measurement procedure and the external circuitry.…”

“…25 In the extreme "quantum transport" limit, where L φ is larger than the localization length ξ, quantum interference destroys the quantization in the insulator and leads to a divergence of ρ xy in the thermodynamic limit. 26,27,28,31 The puddle size is of order l el , and since close to the transition ξ is typically much larger than l el there is an intermediate range where the theory is practically not decisive about the behavior of ρ xy (especially in view of its wide distribution). The experimental data, 34 which mostly accumulate within this intermediate range (where ρ xx increases by at most one order of magnitude), possibly provide evidence for the stability of the QHI behavior in the entire region where ξ > L φ .…”

Classical percolation fingerprints in the high temperature regime of the quantum Hall effect

“…Percolative spatial structures for the local density of states taking place at the transition between Hall plateaus have also been clearly identified in this local probe experiment [9]. Signatures of percolation in transport properties have been mainly discussed in the literature [11][12][13][14][15][16][17] at very low temperatures (typically below T = 1 K), when several quantum mechanical effects (tunneling, quantum coherence, etc) play a role [18][19][20][21][22][23][24][25][26] and complicate the analysis both theoretically and experimentally. However, if the localization mechanism for the QHE is classical in nature, we expect these percolative features at high magnetic fields to be also observable at much higher temperatures, in a classical transport regime.…”