Quantized periodic orbits in large antidot arrays

The resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathit{x}\mathit{x}}$ measured in large antidot arrays as a function of an applied perpendicular magnetic field B displays distinct quantum oscillations at very low temperatures. These oscillations characteristically differ from conventional Shubnikov-de Haas oscillations which are periodic in 1/B. A crossover to B periodic oscillations at low B discloses the influence of the imposed potential. Applying semiclassical periodic orbit theory to the nonintegrable (chaotic) electron motion in the antidot lattice we attribute these phenomena to the quantization of few fundamental periodic orbits.