Quantum and classical surface-acoustic-wave-induced magnetoresistance oscillations in a two-dimensional electron gas

We study theoretically the geometrical and temporal commensurability oscillations induced in the resistivity of two-dimensional electrons in a perpendicular magnetic field by surface acoustic waves (SAWs). We show that there is a positive anisotropic dynamical classical contribution and an isotropic nonequilibrium quantum contribution to the resistivity. We describe how the commensurability oscillations modulate the resonances in the SAW-induced resistivity at multiples of the cyclotron frequency. We study the effects of both short-range and long-range disorder on the resistivity corrections for both the classical and quantum nonequilibrium cases. We predict that the quantum correction will give rise to zero-resistance states with associated geometrical commensurability oscillations at large SAW amplitude for sufficiently large inelastic scattering times. These zero resistance states are qualitatively similar to those observed under microwave illumination, and their nature depends crucially on whether the disorder is short or long range. Finally, we discuss the implications of our results for current and future experiments on two-dimensional electron gases.

Figure 1

Comparison of electron motion in a static and a dynamic periodic potential. When the forces on opposite sides of the orbit are in the same direction, there is a maximum in the magnetoresistance. The horizontal lines correspond to maximum positive (solid lines) and maximum negative (dot-dashed lines) values of the field. In the dynamic case the direction of the field oscillates with frequency $\omega$. Thus, when $\omega$ is an odd multiple of the cyclotron frequency ${\omega }_c$, there is an interchange of the resistance maxima and minima as compared to a static potential.

Figure 2

Magnetoresistance for a short-range potential using the parameters of Ref. 1, and assuming $\omega =2\pi \times 10\mathrm{GHz}$ $(\omega \tau =7)$ and ${\mathrm{v}}_F∕s=63$. We choose a dimensionless SAW amplitude of $\epsilon =0.01$.

Figure 3

Magnetoresistance for a short-range potential using the parameters of Ref. 3, and assuming $\omega =2\pi \times 10\mathrm{GHz}$, which implies $\omega \tau =60$ and ${\mathrm{v}}_F∕s=84$. We choose $\epsilon =0.001$, a factor of 10 less than in Fig. 2.

Figure 4

Magnetoresistance correction for small-angle scattering, with $\omega \tau =7$, ${\mathrm{v}}_F∕s=63$, and $\mathcal{E}=0.02$. The curve is determined by splicing the expressions for the resistance in the strong and weak damping limits (${\omega }_c{\tau }^{*}<1$ and ${\omega }_c{\tau }^{*}>1$, respectively), which are indicated in the figure.

Figure 5

Magnetoresistance correction for small-angle scattering, with $\omega \tau =60$, ${\mathrm{v}}_F∕s=84$, and $\epsilon =0.003$. The curve is determined by splicing the expressions for the resistance in the weak and strong damping limits, which are indicated in the figure.

Figure 6

Magnetoresistance correction for small-angle scattering, with $\omega \tau =600$, ${\mathrm{v}}_F∕s=84$, and $\epsilon =0.002$. The curve is a splice of the formulae for the strong and weak damping limits, and the range of validity for each region is indicated.

Figure 7

Quantum contribution to the magnetoresistance for $\omega \tau =7$, $v_F∕s=63$ and $\omega \tau =60$, ${\mathrm{v}}_F∕s=84$, both with $\omega {\tau }_q=6$, $\epsilon =0.0015$, and $\omega {\tau }_{\mathrm{in}}=302$.

Figure 8

Quantum contribution to magnetoresistance for $\omega \tau =7$, $v_F∕s=63$ and for $\omega \tau =60$, ${\mathrm{v}}_F∕s=84$. In both cases $\omega {\tau }_q=6$, $\epsilon =0.003$, and $\omega {\tau }_{\mathrm{in}}=302$. The arrows indicate the range of validity of the results.