Transport studies of reentrant integer quantum Hall states forming in the two-dimensional electron gas

The two dimensional electron gas subjected to a magnetic field has been a model system in contemporary condensed matter physics which generated many beautiful experiments as well as novel fundamental concepts. These novel concepts are of broad interests and have benefited other fields of research. For example, the observations of conventional odd-denominator fractional quantum Hall states have enriched many-body physics with important concepts such as fractional statistics and composite fermions. The subsequent discovery of the enigmatic even-denominator ν=5/2 fractional quantum Hall state has led to more interesting concepts such as non-Abelian statistics and pairing of composite fermions which can be intimately connected to the electron pairing in superconductivity. Moreover, the observations of stripe phases and reentrant integer quantum Hall states have stimulated research on exotic electron solids which have more intricate structures than the Wigner Crystal. ^ In contrast to fractional quantum Hall states and stripes phases, the reentrant integer quantum Hall states are very little studied and their ground states are the least understood. There is a lack of basic information such as exact filling factors, temperature dependence and energy scales for the reentrant integer quantum Hall states. A critical experimental condition in acquiring this information is a stable ultra-low temperature environment. In the first part of this dissertation, I will discuss our unique setup of 3He immersion cell in a state-of-art dilution refrigerator which achieves the required stability of ultra-low temperature. With this experimental setup, we are able to observe for the first time very sharp magnetotransport features of reentrant integer quantum Hall states across many Landau levels for the first time. I will firstly present our results in the second Landau level. The temperature dependence measurements reveal a surprisingly sharp peak signature that is unique to the reentrant integer quantum Hall states. Such a peak signature allows us to define the energy scale of reentrant integer quantum Hall state. An analysis of the energy scales indicate the collective nature of electron solid states. In the following I will present our results in the third Landau level and higher Landau levels which are used in testing the bubble theory predictions for the reentrant integer quantum Hall states. Currently there is no direct experimental probe of the microscopic structures of the reentrant integer quantum Hall states. Instead, by contrasting their energy scales, we find that certain predictions of the bubble theory are at odds with experimental data in the low Landau level limit. Furthermore, an orbital dependent energy scale from the second Landau level to the fifth Landau level is found which will provide useful insights in determining the bubble structures of these reentrant integer quantum Hall states. ^ It must be appreciated that the reentrant integer quantum Hall states have only been observed in the cleanest GaAs/AlGaAs samples. While the highest electron mobility has been achieved in this system by Molecular Beam Epitaxy technique, further improvements are still necessary to facilitate the study of fragile many-body ground states. However, it is little understood that how different disorder which limits the electron mobility affects the strength of the many-body ground states. In the second part of this dissertation, I will present our work on the impact of alloy disorder on the ν=5/2 fractional quantum Hall state. This work is conducted in a series of specially engineered GaAs/AlGaAs samples with controllable alloy disorder. We are able to quantitatively measure the suppression of the ν=5/2 fractional quantum Hall state by alloy disorder scattering. Surprisingly, the ν=5/2 state is found to develop at significantly reduced mobility compared with the empirical mobility threshold according to prior experiments. An analysis of the results indicates that the short-range alloy disorder and the long-range Coulomb disorder play different roles in the formation of the ν=5/2 fractional quantum Hall state

Contrasting Energy Scales of the Reentrant Integer Quantum Hall States

We report drastically different onset temperatures of the reentrant integer quantum Hall states in the second and third Landau level. This finding is in quantitative disagreement with the Hartree-Fock theory of the bubble phases which is thought to describe these reentrant states. Our results indicate that the number of electrons per bubble in either the second or the third Landau level is likely different than predicted

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

We report quantitative measurements of the impact of alloy disorder on the $\nu=5/2$ 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 $\nu=5/2$ state is suppressed with alloy scattering. To our surprise, in samples with alloy disorder the $\nu=5/2$ 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

Growth and electrical characterization of Al0.24Ga0.76As/AlxGa1-xAs/Al0.24Ga0.76As modulation-doped quantum wells with extremely low x

We report on the growth and electrical characterization of modulation-doped Al0.24Ga0.76As/AlxGa1-xAs/Al0.24Ga0.76As quantum wells with mole fractions as low as x = 0.00057. Such structures will permit detailed studies of the impact of alloy disorder in the fractional quantum Hall regime. At zero magnetic field, we extract an alloy scattering rate of 24 ns(-1) per% Al. Additionally, we find that for x as low as 0.00057 in the quantum well, alloy scattering becomes the dominant mobility-limiting scattering mechanism in ultra-high purity two-dimensional electron gases typically used to study the fragile nu = 5/2 and nu = 12/5 fractional quantum Hall states. (C) 2013 AIP Publishing LLC

Frequency-Dependent Escherichia coli Chemotaxis Behavior

We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies

Frequency-Dependent Escherichia coli Chemotaxis Behavior

We study Escherichia coli chemotaxis behavior in environments with spatially and temporally varying attractant sources by developing a unique microfluidic system. Our measurements reveal a frequency-dependent chemotaxis behavior. At low frequency, the E. coli population oscillates in synchrony with the attractant. In contrast, in fast-changing environments, the population response becomes smaller and out of phase with the attractant waveform. These observations are inconsistent with the well-known Keller-Segel chemotaxis equation. A new continuum model is proposed to describe the population level behavior of E. coli chemotaxis based on the underlying pathway dynamics. With the inclusion of a finite adaptation time and an attractant consumption rate, our model successfully explains the microfluidic experiments at different stimulus frequencies