ν=5/2Fractional Quantum Hall State in the Presence of Alloy Disorder

Abstract

We report quantitative measurements of the impact of alloy disorder on the ν = 5/2 fractional quantum Hall state. Alloy disorder is controlled by the aluminum content x in the Al(x)Ga(1-x)As channel of a quantum well. We find that the ν = 5/2 state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the ν = 5/2 state appears at significantly reduced mobilities when compared to samples in which alloy disorder is not the dominant scattering mechanism. Our results highlight the distinct roles of the different types of disorder present in these samples, such as the short-range alloy and the long-range Coulomb disorder.

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

“…Our results show that Landau-level mixing lowers energy gaps, thereby bringing theoretical estimates closer to experimental measurements [2][3][4][5][6][7][8][9][10]12,[14][15][16][17][18][19][20][21][22][23] of the transport gap. Furthermore, the strong suppression of the gap as a function of the Landau-level-mixing strength that we observe is in good qualitative agreement with the experimental findings presented in Fig.…”

“…Therefore, they may strongly overlap at these system sizes, thereby leading to a finite gap for finite-size systems [78]. Hence, the extrapolation to the thermodynamic limit might be a much more delicate procedure then previously appreciated and, in fact, could point to a potential reason for the long-noticed discrepancy between calculated energy gaps and experimentally measured gaps [2][3][4][5][6][7][8][9][10]12,[14][15][16][17][18][19][20][21][22][23].…”

High-temperature resistivity measured at ν=52 as a predictor of the two-dimensional electron gas quality in the N=1 Landau level

“…3 increases. For the largest 1/ρ 5/2 , where ρ 5/2 is 39Ω, ∆ 5/2 reaches 570mK, among the largest gaps at this density ever reported in literature [7,11,20]. Here, in this comparison of different samples with the same density but different levels of disorder, we also observe a strong correlation between ∆ 5/2 and ρ 5/2 , indicating that ρ 5/2 is sensitive to the scattering mechanisms that limit ∆ 5/2 .…”

“…A particularly illuminating experiment is detailed in Ref. [7]: it was found that intentionally placing short-range disorder directly in the quantum well drastically reduced mobility but had a comparatively small effect on ∆ 5/2 , confirming that µ is limited by short-range disorder while ∆ 5/2 is more sensitive to long-range disorder from remote impurities. The fact that both ∆ 5/2 and ρ 5/2 are sensitive to long-range disorder from remote impurities explains the strong correlation we observe between the two quantities and the lack of correlation with µ.…”

“…This design has been shown to yield the largest gap energy for the ν = 5/2 FQHS [4,7,9,10]. It is believed [2] that low conductivity electrons confined in the X-band of the AlAs barriers surrounding the narrow GaAs doping wells screen potential fluctuations caused by remote donor impurities, promoting expression of large gap FQHS in the N=1 LL.…”