Elastic scattering and absorption of surface acoustic waves by a quantum dot

Knäbchen, Andreas; Levinson, Y.; Entin‐Wohlman, O.

doi:10.1103/physrevb.55.5325

Cited by 7 publications

(6 citation statements)

References 20 publications

(49 reference statements)

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“…The a.c. potential created by a SAW propagating in the x direction is δU (r, t) = A(t) exp i(qx − ω 0 t) + c.c., where the amplitude A(t) is a stationary, slowly varying, random function. This potential is screened by the electrons of the 2DEG [8]. In the wide part of the PC the screening strongly reduces the potential (by the factor qa B , where a B is the Bohr radius), while in the narrow part screening is weak.…”

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confidence: 99%

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Acoustoelectric Current and Pumping in a Ballistic Quantum Point Contact

2000

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The acoustoelectric current induced by a surface acoustic wave (SAW) in a ballistic quantum point contact is considered using a quantum approach. We find that the current is of the "pumping" type and is not related to drag, i.e. to the momentum transfer from the wave to the electron gas. At gate voltages corresponding to the plateaus of the quantized conductance the current is small. It is peaked at the conductance step voltages. The peak current oscillates and decays with increasing SAW wavenumber for short wavelengths. These results contradict previous calculations, based on the classical Boltzmann equation.The interaction of surface acoustic waves (SAW) with electrons in a two dimensional electron gas (2DEG) has recently attracted much attention. In particular the acoustoelectric effect (d.c. current driven by the SAW) was investigated experimentally in a point contact (PC) defined in GaAs/AlGaAs heterostructure by a split gate [1][2][3]. Most of the theoretical considerations of this effect were classical, based on the Boltzmann equation for electrons in a 1D channel, with the SAW considered as a classical force [1,4] or as a flux of monochromatic surface phonons [5,6]. Such an approach is valid only when the channel length is much longer than the electron Fermi wavelength and when the electron diffraction at the channel ends can be neglected. In this picture the acoustoelectric current results from the drag of electrons by the SAW. Its value is determined by the competition between the momentum transfer from the SAW to the 2DEG and the momentum relaxation due to impurity scattering [1,4] or due to electron escape from the PC [4-6], for a ballistic PC.A quantum approach was used in [7], but only PC's of length short compared to the SAW wavelength were considered for the experimentally relevant low frequencies. We present here a quantum description of the problem, based on a different formalism, which allows a more general consideration and leads to results qualitatively different from those given by the classical approach. In particular, we find that the drag mechanism is not valid for the quantum acoustoelectric current, and that the reflection of the elctrons within the PC is crucial for producing the SAW effect. Unfortunately the results of the experiments do not allow to reach a definite conclusion about the mechanism of the acoustoelectric current.Consider a nanostructure (NS) of arbitrary geometry (e.g. a PC) where the 2DEG is confined by a potential U (r) and is attached to terminals α (with no voltage bias). The NS is exposed to a random a.c. potential δU (r, t), produced by a gate or by radiation, infrared or acoustic, and localized within the NS. This a.c. potential induces a current through the NS, the d.c. component of which is the acoustoelectric current or the photovoltaic current, depending on the nature of the radiation. Using time-dependent scattering states (see below for details), we find that the d.c. current J β entering terminal β is given by (e < 0,h = 1)The properties of the a.c. pote...

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confidence: 99%

“…This potential is screened by the electrons of the 2DEG [8]. In the wide part of the PC the screening strongly reduces the potential (by the factor qa B , where a B is the Bohr radius), while in the narrow part screening is weak.…”

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confidence: 99%

Acoustoelectric Current and Pumping in a Ballistic Quantum Point Contact

2000

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“…6 considers bulk phonons, for which, as shown in Ref. 12, the electron-phonon interaction matrix elements have a different q-dependence, compared to surface phonons.…”

Section: Comparison With Previous Approachesmentioning

confidence: 99%

Acoustoelectric effect in a finite-length ballistic quantum channel

2000

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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 r1 and r2 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 r1 and r2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r1 and r2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of 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 non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.

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“…Consequently, the screening is neither sensitive to the symmetry of the system (β = 1, 2, 4) nor depends on the discreteness of the spectrum. It is therefore natural that the dielectric function reduces to its familiar expression for a diffusive system, taken in the limits ω → 0 and q ∼ L −1 , i.e., ε ≃ L/a B ≫ 1 [22], where a B is the Bohr radius.…”

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“…It is therefore natural that the dielectric function reduces to its familiar expression for a diffusive system, taken in the limits ω → 0 and q ∼ L −1 , i.e. ε L/a B 1 [22], where a B is the Bohr radius. For typical sound frequencies, qL 1, and, hence, the matrix element simplifies to M mn = iV ω q m|r|n .…”

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confidence: 99%