The Effect of a Magnetic Field on the Acoustoelectric current in a Narrow Channel

The effect of a perpendicular magnetic field on the quantized current induced by a surface acoustic wave in a quasi-1D channel is studied. The channel has been produced experimentally in a GaAs heterostructure by shallow etching techniques and by the application of a negative gate voltage to Schottky split gates. Commensurability oscillations of the quantized current in this constriction have been observed in the interval of current between quantized plateaus. The results can be understood in terms of a moving quantum dot with the electron in the dot tunneling into the adjacent two-dimensional region. The goal is to explain qualitatively the mechanism for the steplike nature of the acoustoelectric current as a function of gate voltage and the oscillations when a magnetic field is applied. A transfer Hamiltonian formalism is employed.Comment: 5 pages, 2 figure

Acoustoelectric effect in a finite-length ballistic quantum channel

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 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.Comment: 7 pages, 2 figure

Giant Oscillations of Acoustoelectric Current in a Quantum Channel

A theory of d.c. electric current induced in a quantum channel by a propagating surface acoustic wave (acoustoelectric current) is worked out. The first observation of the acoustoelectric current in such a situation was reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors observed a very specific behavior of the acoustoelectric current in a quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a split-gate depletion -- giant oscillations as a function of the gate voltage. Such a behavior was qualitatively explained by an interplay between the energy-momentum conservation law for the electrons in the upper transverse mode with a finite temperature splitting of the Fermi level. In the present paper, a more detailed theory is developed, and important limiting cases are considered.Comment: 7 pages, 2 Postscript figures, RevTeX 3.

Acoustoelectric effects in quantum constrictions

A dc current induced in a quantum constriction by a traveling acoustic wave (or by non-equilibrium ballistic phonons) is considered. We show that in many important situations the effect is originated from acoustically-induced scattering between the propagating and reflecting states in the constriction. Two particular regimes corresponding to relatively high and low acoustic frequencies are discussed. In the first regime, the acoustoelectric effect in a smooth constriction can be understood by semi-classical considerations based on local conservation laws. For the low frequency regime, we show that the acousto-conductance is closely related to the zero field conductance. The qualitative considerations are confirmed by numerical calculations both for smooth and abrupt channels.Comment: 10 pages, RevTeX, 9 postscript figures, submitted to Phys. Rev.

Nonlinear absorption of surface acoustic waves by composite fermions

Absorption of surface acoustic waves by a two-dimensional electron gas in a perpendicular magnetic field is considered. The structure of such system at the filling factor $\nu$ close to 1/2 can be understood as a gas of {\em composite fermions}. It is shown that the absorption at $\nu =1/2$ can be strongly nonlinear, while small deviation form 1/2 will restore the linear absorption. Study of nonlinear absorption allows one to determine the force acting upon the composite fermions from the acoustic wave at turning points of their trajectories.Comment: 7 pages, 1 figure, submitted to Europhysics letter

Weiss Oscillations in Surface Acoustic Wave Propagation

The interaction of a surface acoustic wave (SAW) with a a two-dimensional electron gas in a periodic electric potential and a classical magnetic field is considered. We calculate the attenuation of the SAW and its velocity change and show that these quantities exhibit Weiss oscillations.Comment: 4 pages REVTEX, 2 figures included as eps file

Nonlinear acousto-electric transport in a two-dimensional electron system

We study both theoretically and experimentally the nonlinear interaction between an intense surface acoustic wave and a two-dimensional electron plasma in semiconductor-piezocrystal hybrid structures. The experiments on hybrid systems exhibit strongly nonlinear acousto-electric effects. The plasma turns into moving electron stripes, the acousto-electric current reaches its maximum, and the sound absorption strongly decreases. To describe the nonlinear phenomena, we develop a coupled-amplitude method for a two-dimensional system in the strongly nonlinear regime of interaction. At low electron densities the absorption coefficient decreases with increasing sound intensity, whereas at high electron density the absorption coefficient is not a monotonous function of the sound intensity. High-harmonic generation coefficients as a function of the sound intensity have a nontrivial behavior. Theory and experiment are found to be in a good agreement.Comment: 27 pages, 6 figure

Surface acoustic wave attenuation by a two-dimensional electron gas in a strong magnetic field

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a strong magnetic field and a smooth random potential with correlation length Lambda and amplitude Delta. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. In accordance with the experimental situation, Lambda is assumed to be much smaller than the sound wavelength 2*pi/q. This restricts the absorption of surface phonons at a filling factor \bar{\nu} approx 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function varepsilon(omega,q) to describe the effect of screening on the electron-phonon coupling. In the low temperature, high frequency regime T << Delta (omega_q*Lambda /v_D)^{alpha/2/nu}, where omega_q is the SAW frequency and v_D is the electron drift velocity, both the attenuation coefficient Gamma and varepsilon(omega,q) are independent of temperature. The classical percolation indices give alpha/2/nu=3/7. The width of the region where a strong absorption of the SAW occurs is found to be given by the scaling law |Delta \bar{\nu}| approx (omega_q*Lambda/v_D)^{alpha/2/nu}. The dependence of the electron-phonon coupling and the screening due to the 2DEG on the filling factor leads to a double-peak structure for Gamma(\bar{\nu}).Comment: 17 pages, 3 Postscript figures, minor changes mad

Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-

In this paper, we propose the quantum spin pumping in quantum spin systems where an applied electric field ($E$) and magnetic field ($H$) cause a finite spin gap to its critical ground state. When these systems are subject to alternating electromangetic fields; $(E,H)=(\sin\frac{2\pi t}{T},\cos\frac{2\pi t}{T})$ and travel along the {\it{loop}} $\Gamma_{\rm{loop}}$ which encloses their critical ground state in this $E$-$H$ phase diagram, the locking potential in the sine-Gordon model slides and changes its minimum. As a result, the phase operator acquires $2\pi$ holonomy during one cycle along $\Gamma_{\rm{loop}}$, which means that the quantized spin current has been transported through the bulk systems during this adiabatic process. The relevance to real systems such as Cu-benzoate and ${\rm{Yb}}_4{\rm{As}}_3$ is also discussed.Comment: 10 pages, 5 figures, to be published in J. Phys. Soc. Jpn. 74 (2005) no. 4. Typos corrected in the revised versio