| 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 mum and 0.8 mum spacings between the gates. However, in our sample, all signatures of the 5/2 state are completely gone in a 0.5 mum 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/e2, while at higher temperatures this plateau does not form. We study the dc-current-bias (Idc) dependence of the plateau-like feature, and find a peak in the differential resistance at I dc = 0 and a dip around Idc ∼ 1.2nA, consistent with quasiparticle tunneling between fractional edge states. In a QPC with 0.5 mum 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. |
