Quantum ballistic and adiabatic electron transport studied with quantum point contacts

We present an experimental and theoretical study of quantum ballistic transport in single quantum point contacts (QPC’s), defined in the two-dimensional electron gas (2DEG) of a high-mobility GaAs/${\mathrm{Al}}_{0.33}$ ${\mathrm{Ga}}_{0.67}$As heterojunction. In zero magnetic field the conductance of quantum point contacts shows the formation of quantized plateaus at multiples of 2${\mathit{e}}^2$/h. The experimental results are explained with a simple model. Deviations from ideal quantization are discussed. The experimental results are compared with model calculations. Energy averaging of the conductance has been studied, both as a function of temperature and voltage across the device. The application of a magnetic field leads to the magnetic depopulation of the one-dimensional subbands in the QPC. It is shown that the zero-field quantization and quantization in high magnetic fields are two limiting cases of a more general quantization phenomenon. We use quantum point contacts to study the high-magnetic-field transport in a 2DEG. Quantum point contacts are used to selectively populate and detect edge channels. The experiments show that scattering between adjacent edge channels can be very weak, under certain circumstances even on length scales longer than 200 μm. This adiabatic transport has resulted in the observation of an anomalous integer quantum Hall effect, in which the quantization of the Hall conductance is not determined by the number of Landau levels in the bulk 2DEG, but by the number of Landau levels in the QPC’s instead. Related effects are the anomalous quantization of the longitudinal resistance and the adiabatic transport through QPC’s in series. A theoretical description for transport in the presence of Shubnikov–de Haas (SdH) backscattering is given. This model explains the experimentally observed suppression of the SdH oscillations due to the selective population or detection of edge channels. Finally, we demonstrate that the combination of a QPC and a bulk Ohmic contact can act as a controllable edge-channel mixer.