Noise in a quantum point contact due to a fluctuating impurity configuration

We propose a theoretical model for the low-frequency noise observed in a quantum point contact (QPC) electrostatically defined in the 2D electron gas at a GaAs-AlGaAs interface. In such contacts electron scattering by soft impurity or boundary potentials coherently splits an incoming wave function between different transverse modes. Interference between these modes has been suggested to explain observed non-linearities in the QPC conductance. In this study we invoke the same mechanism and the time-dependent current due to soft dynamical impurity scattering in order to analyse the low-frequency (telegraph-like) noise which has been observed along with a non-linear conductance. For the simplified case of a channel with two extended (current carrying) modes, a simple analytical formula for the noise intensity is derived. Generally we have found qualitative similarities between the noise and the square of the transconductance. In comparison with the more traditional d.c. transport measurements we believe that noise measurements can provide additional information about the dynamical properties of QPCs.