Quantum Transport in the AlGaAs/GaAs Two Dimensional Electron System at Half-Fillings

Recently great research effort has been put toward the study of strongly correlated electron systems, of particular interest is the intriguing quantum phases at half-filled Landau levels (LL), including the exotic fractional quantum Hall state (FQHS) at filling factor ν = 5/2 in the N = 1 LL, and density modulated phases in high LLs. The state of the art AlGaAs/GaAs heterostructure grown by molecular bean epitaxy provides a superior platform to study these many-body interactions. In this thesis, a brief introduction of different phases in half-filled LLs is given in Chapter 1. The remaining chapters, summarized below, describe detailed study exploring the unique transport properties of these quantum phases. Chapter 2 and 3 of this thesis focus on physics related with filling factor ν = 5/2. As the lack of correlation between mobility and Δ 5/2, the excitation gap of ν = 5/2 FQHS, has been well established in previous experiments, our work aimed at finding metrics as high temperature (T = 0.3 K) predictors of Δ5/2. We first consider quantum lifetime derived from low-field Shubnikov-de Haas (SdH) oscillations as a metric of quality of the two-dimensional electron system (2DES) in GaAs quantum wells that expresses large Δ5/2. In high quality samples small density inhomogeneities dramatically impact the amplitude of SdH oscillations such that the canonical method for determination of quantum lifetime substantially underestimates τq unless density inhomogeneity is explicitly considered. We have developed a method which can be used to determine density inhomogeneity and extract the intrinsic τq by analyzing the SdH oscillations. However, even after accounting for inhomogeneity, τ q does not correlate well with sample quality as measured by Δ 5/2. The measurements and analysis of quantum lifetime are detailed in Chapter 2. In Chapter 3, we define, analyze and discuss the utility of a different metric ρ5/2, the resistivity at ν = 5/2 measured at T = 0.3 K, as a high temperature predictor of Δ5/2. This high-field resistivity reflects the scattering rate of composite fermions. Good correlation between Δ5/2 and ρ5/2 is observed in both a density tunable device and in a series of identically structured wafers with similar density but vastly different mobility. This correlation can be explained by the fact that both ρ5/2 and Δ 5/2 are sensitive to long range disorder from remote impurities, while mobility is sensitive primarily to disorder localized near the quantum well. Chapter 4 represents the study of anisotropic transport in high Landau levels. Theory has predicted the existence of a liquid crystal smectic phase that breaks both rotational and translational symmetries in the quantum Hall regime. However, previous experiments in 2DES are most consistent with an anisotropic nematic phase breaking only rotational symmetry. Here we report three transport phenomena at half-filling in ultra-low disorder 2DES: a non-monotonic temperature dependence of the sample resistance, dramatic onset of large time-dependent resistance fluctuations, and a sharp feature in the differential resistance suggestive of depinning. These data suggest that a sequence of symmetry-breaking phase transitions occurs as temperature is lowered: first an transition from an isotropic liquid to a nematic phase and finally to a liquid crystal smectic phase. Physical parameters related with the nematic to smectic phase transition, for example, disorder, in-plane magnetic field, 2DES density, etc., are discussed in this chapter as well. Chapter 5 discusses temperature-induced transport asymmetry of both the zero-bias magnetoresistance Rxx and the differential resistance dVxx/dI along the hard transport direction around filling factor ν = 9/2 . At high temperature, T = 100 mK, both of them are symmetric around ν = 9/2 . However, as temperature is decreased towards T = 10 mK both of them become asymmetric: the Rxx peak shifts to lower magnetic field away from exact half-filing, and dVxx/dI shows strong non-linearity on the high eld side of the Rxx peak. Our data possibly suggests that a temperature induced breakdown of particle-hole symmetry occurs in smectic phase. At high temperature T = 100 mK where the system behaves as a standard anisotropic nematic, particle-hole symmetry is restored