Acoustoelectric effect in a finite-length ballistic quantum channel

Abstract

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients ${r}_{1}$ and ${r}_{2},$ at both channel ends, are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging ${r}_{1}$ and ${r}_{2}.$ The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of ${r}_{1}$ and ${r}_{2}.$ It is shown that both contributions to the current are nonzero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as a function of $\mathrm{qL}.$ These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of noncoherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.