Flicker noise induced by dynamic impurities in a quantum point contact

We calculate low-frequency noise (LFN) in a quantum point contact (QPC) which is electrostatically defined in a two-dimensional electron gas of a GaAs-Al_xGa_1-xAs heterostructure. The conventional source of LFN in such systems is scattering potentials fluctuating in time acting upon injected electrons. One can discriminate between potentials of different origin—noise may be caused by the externally applied gate- and source-drain voltages, the motion of defects with internal degrees of freedom close to the channel, electrons hopping between localized states in the doped region, etc. In the present study we propose a model of LFN based upon the assumption that there are many dynamic defects in the surroundings of a QPC. A general expression for the time-dependent current-current correlation function is derived and applied to a QPC with quantized conductance. It is shown that the level of LFN is significantly different at and between the steps in a plot of the conductance vs, gate voltage. On the plateaus, the level of noise is found to be low and strongly model dependent. At the steps, LFN is much larger and only weakly model dependent. As long as the system is biased to be at a fixed position relative to the conductance step, we find that the level of noise is independent of the number of conducting modes. From numerical calculations we conclude that the level of noise approximately obeys a power law as a function of frequency for frequencies larger than a threshold. At the steps for frequencies larger than the minimal transition rate for the dynamic impurities, we have S(ω)∝1/ω^0.85. We are convinced that noise measurements will play a crucial role in the course of investigating the effect of the environment in QPC’s.