We study low-frequency noise in selectively doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ quantum point contact and Hall bar structures. Experiments are carried out at 4.2 K and constant magnetic fields where noise in both diagonal and Hall voltages is measured using a four-terminal lock-in technique. In all cases, for low currents and low frequencies, we find the size of excess voltage noise power to be quadratic in current and, furthermore, Hall voltage noise power to be quadratic in magnetic field. Resistance fluctuations of the quantum point contact samples are mostly dominated by a single two-level or multilevel switching event that leads to a Lorentzian noise spectrum, whereas resistance fluctuations of the Hall bar structures exhibit $1/f$ noise, which results from the superposition of many independent switching events. Three possible sources of $1/f$ noise, i.e., fluctuations in carrier density, mobility, and quantum interference corrections, are considered in the analysis of the Hall bar data. From the size of $1/f$ noise in the Hall voltage, we deduce an upper bound for the size of carrier density fluctuations that is so small that we rule out electron trapping as a main source of resistance fluctuations in the quantum point contact structures. Instead, we explain observed low-frequency noise in both mesoscopic and macroscopic structures by fluctuations in the remote impurity configuration.

• Received 31 March 1997

DOI:https://doi.org/10.1103/PhysRevB.56.9813