Evidence for a quantum Hall insulator in an InGaAs/InP heterostructure

Abstract

We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility In0.53Ga0.47As/InP heterostructure. By reversing the direction of the magnetic field (B) we find an averaged Hall resistance ρxy which remains quantized at the plateau value h/e 2 throughout the PI transition. We extract a critical exponent κ ′ = 0.57 ± 0.02 for the PI transition which is slightly different from (and possibly more accurate than) the established value 0.42 ± 0.04 as previously obtained from the plateau-plateau (PP) transitions.One of the fundamental issues in the field of two dimensional electron gases is the nature of the transitions between adjacent quantum Hall plateaus. By measuring the resistance tensor of low mobility In 0.53 Ga 0.47 As/InP heterostructures, Wei et al. [1,2] demonstrated that the quantum Hall steps become infinitely sharp as T → 0, indicating that the transitions between adjacent quantum Hall plateaus (PP transitions) represent a sequence of quantum phase transitions (QPT). Both the maximum slope in the Hall resistance with varying B, (∂ρ xy /∂B) max , and the inverse of the half-width of the longitudinal resistance between two adjacent quantum Hall plateaus, (∆B) −1 , have been shown to follow the power law T −κ as T approaches absolute zero, independent of Landau level index. Here, κ = p/2ν where p denotes the exponent of the phase breaking length ℓ ϕ at finite T (i.e. ℓ ϕ ∼ T −p/2 ) and ν is the critical index for the localization length ξ which is defined at zero T .In order to probe the QPT, it is essential to carry out experiments on samples where the dominant scattering mechanism is provided by short ranged random potential fluctuations [3]. Like in In 0.53 Ga 0.47 As/InP, this produces the widest range in T where quantum criticality is accessible experimentally. At the same time, little is known about the effects of macroscopic sample inhomogeneities which generally complicate experiments on the QPT. The problem of sample inhomogeneities was recently addressed by van Schaijk et al. [4] who investigated the plateau-insulator (PI) transition in the lowest Landau level. The data were taken from the same In 0.53 Ga 0.47 As/InP heterostructure which was previously used in the study of the PP transitions [2].Following the analysis by van Schaijk et al. one can extract different exponents κ and κ ′ from the transport data on the PI transition, dependent on the specific quantity one considers. For example, the longitudinal resistance ρ xx was shown to follow the exponential law [5] ρ xx (ν, T ) ∝ exp(−∆ν/ν 0 (T )). Here, ∆ν = ν − ν c represents the filling fraction ν of the lowest Landau level relative to the critical value ν c ≈ 1 2 and ν 0 (T ) ∝ T κ ′ with an experimental value κ ′ = 0.55 ± 0.05. The numerical value of the exponent κ ′ differs by more than the experimental error from the established "universal" value 0.42 ± 0.05 that was previously extracted from the resistance data on PP transitions [1,2]. In an attempt to understand the difference, van Schaijk et al. poin...

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

“…This is also true if we use a much smaller value of , e.g., = 0.42 previously reported for the PP transitions of these InGaAs/ InP heterostructures. 22,24 We stress that our magnetotransport experiments carried out on different samples [18][19][20]15,27,28 provide solid evidence for an intrinsic critical exponent = 0.58 for the PI transition. The critical exponent is obtained directly from the xx Ϸ 0 ͑͒ data.…”

“…It was prepared in the form of a Hall bar with a channel width W of 650 m and length L between the voltage contacts of ϳ1100 m. Previous magnetotransport experiments carried out on the same sample confirmed scaling in the quantum Hall regime. 15,18,19,24 Reference 24 focused on the PP transitions =4→ 3, 3 → 2, and 2 → 1, for which it was demonstrated that the components of the resistivity tensor obey scaling, i.e., the maximum slope in the Hall resistivity ͑d xy / dB͒ max and the inverse of the half width of xx between adjacent quantum Hall plateaus ͑⌬B͒ −1 both diverge algebraically with temperature as T − with a critical exponent = 0.42. 22 In Ref.…”

“…18 We make use of a comprehensive analysis of the magnetotransport data ͑Refs. 19 and 20͒ in the framework of the scaling theory of the quantum Hall effect, 21 which provides solid evidence that the PI transition occurs in the quantum critical regime.…”

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

“…In this paper, we briefly address the principles of scaling and delineate our methodology to disentangle the quantum critical aspects of the two-dimensional electron gas from the sample dependent effects. Next we review the results of recent high-field magnetotransport studies carried out on different InGaAs/InP heterostructures (HS) [1,6,8,10] and an InGaAs/GaAs quantum well (QW) [10,11] .…”

Fluctuating Hall resistance defeats the quantized Hall insulator

“…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 .…”