Probing Symmetry and Disorder Effects in the Fractional Quantum Hall States of the Second Landau Level

Electrons confined to two dimensions, cooled to cryogenic temperatures, and placed in a strong perpendicular magnetic field exhibit a set of ground states referred to as the fractional quantum Hall states (FQHS). The FQHSs forming in the region called the second Landau level are some of the most exciting states as several theories predict that they are very different from the well understood FQHS in the lowest Landau level. Nonetheless, the nature of these FQHSs continue to evade understanding. In this thesis, a unique ultra-low temperature setup is used to examine the FQHSs of the second Landau level in regimes which have not been studied previously. Additionally, a new instrument was developed for future studies of these exciting FQHSs. In Chapter 2, I describe measurements in a high quality sample in the region of the second Landau level referred to as the upper spin branch at a factor of two lower temperatures than previous measurements in this region. In this region we find a new FQHS at the filling factor ν = 3+1/3. A quantitative study of this new and other FQHS in the upper spin branch reveals a surprising relationship: the relative magnitudes of the energy gaps of the ν = 3+1/3 and 3+1/5 states are reversed when compared to the counterpart states in the lower spin branch at ν = 2+1/3 and 2+1/5. We demonstrate that this reversal is only found to occur in the upper spin branch and cannot be understood within the existing theories. Our results suggest the possibility of new types of FQHSs in this region. In Chapter 3, I examine the even denominator FQHSs at ν = 5/2 and ν = 7/2 in a series of samples with intentionally added alloy disorder. The energy gap of both of these states is suppressed with increased alloy content. Unexpectedly, in contrast to samples with no added disorder, in samples with intentionally added alloy disorder we find that the measured energy gap of the ν = 5/2 FQHS displays a strong correlation with the mobility. Of further surprise, the ν = 5/2 FQHS continues to develop in samples with mobilities greater than μ = 1.7 × 106 cm2/Vs which is a significantly lower mobility threshold than what is seen for samples with no added disorder. We conclude that the contrasting behavior of the ν = 5/2 FQHS in clean and dirty samples result from different the influence on the ν = 5/2 state from different sources of disorder. We then examine the suppression of the energy gap of the even denominator FQHS within a phenomenological model of disorder induced energy level broadening. It is found that the disorder induced broadening of these energy levels correlates with the alloy scattering rate. For the first time at the even denominator FQHSs, we establish a quantitative, linear relationship between transport scattering rate and the broadening width of the energy levels. Finally, in Chapter 4, I describe a new dc SQUID-based current amplifier which is capable of performing Johnson noise limited measurements in the fractional quantum Hall regime. An impedance matching transformer is placed at the input of a commercially available dc SQUID ammeter. This circuit exhibits an extremely low amplifier noise of 2.3fA/√Hz. We use this circuit to measure the Johnson noise of a 3.1 kΩ resistor and find that the Johnson noise of the resistor dominates to temperatures as low as 15.8 mK. This instrument will enable future high resolution, low noise measurements at decreased excitation as well as Johnson noise and shot noise measurements in the fractional quantum Hall regime