Electron transport in GaAs heterostructures at various magnetic field strengths

This thesis describes two sets of experiments which explore transport in a two-dimensional electron gas in the presence of a magnetic field. We used nanofabrication techniques to make samples on GaAs/AlGaAs heterostructures, and measured the samples at cryogenic temperatures using ac-lock-in techniques. In the first set of experiments---the low-field experiments---we studied the effect of spin-orbit coupling. We tuned the strength of spin-orbit coupling from the weak localization regime to the antilocalization regime using in situ gate control. Using a new theory, we separately extracted the values for the three material-dependent spin-orbit constants. We also measured the average and variance of conductance in assorted quantum dots, with and without strong spin-orbit coupling, and found quantitative agreement with recent random matrix theory predictions, as long as we also properly included the effects of parallel magnetic field. In the second set of experiments---the high-field experiments---we studied the transport properties of quantum point contacts (QPC) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits excellent bulk fractional quantum Hall effect, including a strong plateau in the Hall resistance at Landau level filling fraction v = 5/2. We demonstrate that the v = 5/2 state can survive in QPCs with 1.2 [mu]m and 0.8 [mu]m spacings between the gates. However, in our sample, all signatures of the 5/2 state are completely gone in a 0.5 [mu]m QPC. We study the temperature dependence at v = 5/2 in the QPC and find two distinct regimes: at temperatures below 19 mK a we find a plateau-like feature with resistance near (but above) the bulk quantized value of 0.4 h/e 2 , while at higher temperatures this plateau does not form. We study the dc-current-bias ( I dc ) dependence of the plateau-like feature, and find a peak in the differential resistance at I dc = 0 and a dip around I dc ~ 1.2nA, consistent with quasiparticle tunneling between fractional edge states. In a QPC with 0.5 [mu]m spacing between the gates, we do not observe a plateau-like feature at any temperature, and the I dc characteristic is flat for the entire range between v = 3 and v = 2.