Absorption of surface acoustic waves by quantum dots: Discrete spectrum limit

Abstract

PACS. 72.50.+b-Acoustoelectric effects. PACS. 73.20.Fz -Weak localization effects.Abstract. -The absorption of surface acoustic waves (SAW's) by an array of quantum dots in which the mean level spacing ∆ is larger than the sound frequency ω, the temperature T , and the phase breaking rate τ −1 Typeset using EURO-L a T E X

Attenuation of surface acoustic waves by quantum dots

“…DISCRETE SPECTRUM Since the phonon energy is now smaller than the typical separation of adjacent well resolved levels (w, 7';' < A ) , the absorption of energy from the SAW field is very different from the case of a continuous spectrum. We find (Knabchen et al 1997a) that one may distinguish between three different contributions to r: firstly resonant direct transitions; secondly direct transitions due to the tails of the broadened levels; thirdly absorption due to Debye (or relaxational) processes.…”

“…because then the dots are approximately translationally invariant. For qL << 1, the attenuation associated with elastic scattering is given by (w << E,) (Knabchen et al 1997a) where the dependence on q4 is typical for Rayleigh scatting. The ratio of Tsc to r (cf.…”

“…Interesting problems which have not been discussed here include the screening of the SAW field due to the electrostatic coupling between the dots as well as the crossovers between the different pure symmetries and the discrete-and the continuousspectrum limits (Knabchen et al 1997a).…”

“…M I 2 is the corresponding matrix element with the piezoelectric electron-phonon coupling and is independent of energy as long as t < E, (Knabchen et al 1997a). The difference between the occupation numbers is -,f2 = tanh ( t / 2 T ) in a canonical ensemble.…”

“…However, as shown by Blanter (1996), the former yields a vanishingly small rate when E , T < A . The rate re is then determined by electron-phonon processes which yield (Knabchen et al 1997a) where Vph is the phonon density of states and M ( E ) denotes the matrix element for the piezoelectric interaction with three-dimensional thermal phonons. Equation (9) has to be averaged over different disorder realizations with the level correlation function R ( E ) which favours typical spacings t rv A .…”