Screening of the surface-acoustic-wave potential by a metal gate and the quantization of the acoustoelectric current in a narrow channel

Abstract

The piezoelectric potential accompanying a surface acoustic wave (SAW) launched on the surface of a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructure is calculated. The screening due to a narrow metal gate on the surface is included and a closed form analytic solution for the SAW potential is obtained. This potential is used to calculate the SAW-induced acoustoelectric current in a quasi-one-dimensional electron channel formed in the heterostructure by the split gates. At gate voltages beyond the pinch off, electrons are transported through the channel in local quantum wells formed by the SAW potential. In recent experiments, Talyanskii et al. [Phys. Rev. B 56, 15 180 (1997)] found that, in this regime, the acoustoelectric current I versus the gate voltage displays a step-like behavior. The values of the current on the plateaus are quantized with $I=nef$ where e is electron charge, f is the SAW frequency, and n is the number of electrons transported through the channel per SAW cycle. Using a simple model for the electrostatic barrier in the channel, we show that when one electron is trapped in the quantum well, the current depends on a parameter $\ensuremath{\beta}$ defined as the ratio of the piezoelectric potential amplitude to the height of the electrostatic barrier. When $\ensuremath{\beta}$ increases, the current rapidly increases from zero to its quantized value $I=ef.$ The obtained results explain the first current plateau and qualitatively agree very well with the experiment.