Quantized acoustoelectric current in a finite-length ballistic quantum channel: The noise spectrum

Fluctuations in the acoustoelectric current, induced by a surface acoustic wave propagating along a ballistic quantum channel, are considered. We focus on the large-wave-amplitude case, in which it has been experimentally found that the current is quantized, and analyze the noise spectrum. A phenomenological description of the process, in terms of a random pulse sequence, is proposed. The important ingredients of this description are the probabilities $p_n$ for a surface acoustic wave well to capture n electrons. It is found that from the noise characteristics one can obtain these probabilities, and also estimate the typical length scales of the regions in which the electrons are trapped.