Evolution from commensurability to size-effects structures in three-dimensional billiards

Abstract

We calculated the classical electron dynamics of three-dimensional electrons in a billiard system in tilted magnetic field and analyzed the evolution of trajectories in phase space by means of Poincaré space of sections. The low field magnetoresistance ρ xx was calculated through linear response theory and found that nonlinear resonances between the cyclotron radius Rc, the antidot lattice period a, and the well width W , are reflected in the observed magnetoresistance peaks.