Date of Award

Spring 2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Michael Manfra

Committee Chair

Michael Manfra

Committee Member 1

Chris H. Greene

Committee Member 2

Gabor Csathy

Committee Member 3

Ken Ritchie

Committee Member 4

John Reno


The unparalleled quality of GaAs/AlGaAs heterostructures grown by molecular beam epitaxy has enabled a wide range of experiments probing interaction effects in two-dimensional electron and hole gases. This dissertation presents work aimed at further understanding the key material-related issues currently limiting the quality of these 2D systems, particularly in relation to the fractional quantum Hall effect in the 2nd Landau level and spin-based implementations of quantum computation.^ The manuscript begins with a theoretical introduction to the quantum Hall effect which outlines the experimental conditions necessary to study the physics of interest and motivates the use of the semiconductor growth and cryogenic measurement techniques outlined in chapters 2 and 3, respectively. In addition to a generic introduction to the molecular beam epitaxy growth technique, chapter 2 summarizes some of what was learned about the material purity issues currently limiting the low temperature electron mobility. Finally, a series of appendices are included which detail the experimental methods used over the course of the research.^ Chapter 4 presents an experiment examining transport in a low density two-dimensional hole system in which the hole density could be varied by means of an evaporated back gate. At low temperature, the mobility reached a maximum of 2.6 × 106 cm2/Vs at a density of 6.2 × 1010 cm-2 which is the highest reported mobility in a two-dimensional hole system to date. In addition, it was found that the mobility as a function of density did not follow a power law with a single exponent. Instead, it was found that the power law varied with density, indicating a cross-over between dominant scattering mechanisms at low density and high density. At low density the mobility was found to be limited by remote ionized impurity scattering, while at high density the dominant scattering mechanism was found to be background impurity scattering.^ Chapter 5 details an experiment examining transport in a series of two-dimensional hole gases in which the dopant setback distance and the Al mole fraction in the barriers of the quantum well were varied. The hole density was tuned in this way from 0.18 – 1.9 × 1011 cm-2. Surprisingly, the mobility at T = 0.3 K was found to peak at 2.3 × 10 6 cm-2at an intermediate density of 6.5 × 10 10 cm-2. Self-consistent Schrödinger/Poisson calculations were performed for each wafer to examine the scattering rates due to a variety of potentials at low temperature. The drop in mobility at high density could be accounted for with the inclusion of interface roughness scattering, but using the same interface roughness scattering parameters for similar two-dimensional electron gases produced inconsistent results. This leaves open the possibility of contributions from other scattering mechanisms in the hole samples at high density.^ Chapter 6 presents an in-depth study of in-situ backgated two-dimensional gases used for studying the fragile fractional quantum Hall states in the 2nd Landau level. It was found that leakage currents as small as 4 pA could cause noticeable heating of the electron gas if the lattice was not properly thermally anchored to the cryostat. However, it was also found that when the heterostructure design and device fabrication recipe were properly optimized, gate voltages as large as 4 V could be applied before the leakage turned on, allowing the density to be tuned from full depletion to over 4 × 1011 cm-2. As a result, heating effects at dilution refrigerator temperatures were negligible and the gap at ν = 5/2 could be tuned continuously with density to a maximum value of 625 mK, the largest reported to date. An unusual evolution of the reentrant integer quantum Hall states as a function of density is also reported. Such devices should prove useful for the study of electron correlations in nanostructures in the 2nd Landau level.