| This dissertation describes the use of time-resolved measurement techniques to investigate the high-frequency transport properties of split-gate quantum point contacts (QPCs). A specially-designed cryostat, with signal lines impedance matched to 50 O, was constructed for these experiments and allowed for the delivery of high-frequency signals to the QPCs with minimal reflection. This cryostat could be used for measurements at 4.2 K, while providing access to magnetic fields of up to 8 T. To investigate the limitations of our measurement setup, the transient response of a high-mobility two-dimensional electron gas (2DEG) was measured in the quantum-Hall regime. The results of these studies showed the time resolution of our setup to be in the sub-nanosecond range. To measure the transient response of the QPCs, long (400-ns duration) voltage pulses with short (≥ 2 ns) rise times were applied to their input and the form of their output pulse was studied as the QPC gate bias was varied. Conductance values extracted from the steady state value of the output pulse were generally found to be in agreement with those from (quasi-) DC (lock-in) measurements. At the rising/falling edge of the input pulse, however, the output pulse was found to exhibit significant overshoot/undershoot, followed by an exponential decay. The time constant of this decay (∼30--40 ns) did not vary significantly with QPC conductance or input-pulse amplitude. The time constant rapidly vanished, however, when the bias applied to the gates was set back to zero and the system transitioned from a QPC to a 2DEG. These features indicate the presence of a significant capacitance (∼ nF) in parallel with the QPC channel, which therefore functions as a compact RC nanocircuit. Although the origin of this capacitance is unclear at present, we believe that it is intrinsic to the split-gate system. |
