Commensurate and rosette-shaped electron orbits probed by surface acoustic wave attenuation

We have investigated the interaction between a surface acoustic wave (SAW) and a two-dimensional (2D) electron gas subject to a strong 2D periodic modulation. At low magnetic fields, much below the onset of Shubnikov-de Haas oscillations, we observe a minimum in the SAW attenuation near ~0.15 T, which we interpret as the signature of the peaks in magnetoresistance seen in such systems in the regime where commensurate electron orbits circle one or more antidots. Additional structure is observed at higher fields, which we assign to the formation of stationary rosette-shaped electron orbits that encircle a single antidot. A quantitative analysis of these high-field structures yields reasonable values for the antidot spacings, which increase as the square root of the carrier concentration.