PERIODIC-ORBIT THEORY OF QUANTUM TRANSPORT IN ANTIDOT LATTICES

In a recent experiment Weiss et al. (Phys. Rev. Lett., 70 (1993) 4118) observed novel quantum oscillations in the magnetoconductance of large antidot lattices whose classical dynamics is chaotic. Using a semiclassical approach to the Kubo formula, we derive analytical expressions for quantum corrections to the conductivity in terms of the classical periodic orbits of the system which explain the observations by Weiss et al. The contribution from each periodic orbit oscillates as a function of magnetic field and Fermi energy with the phase given by the classical action. The amplitude is determined by the stability of the orbit and disorder-dependent velocity correlations. We also show that these quantum oscillations are related to Shubnikovde Haas oscillations.