Frequency-dependent magnetotransport and particle dynamics in magnetic modulation systems

We analyze the dynamics of a charged particle moving in the presence of spatially modulated magnetic fields. From Poincaresurfaces of section and Liapunov exponents for characteristic trajectories we find that the fraction of pinned and runaway quasiperiodic orbits vs chaotic orbits depends strongly on the ratio of cyclotron radius to the structure parameters, as well as on the amplitude of the modulated field. We present a complete characterization of the dynamical behavior of such structures, and investigate the contribution to the magne- toconductivity from all different orbits using a classical Kubo formula. Although the dc conductivity of the system depends strongly on the pinned and runaway trajectories, the frequency response reflects the topology of all different orbits, and even their unusual temporal behavior. @S0163-1829~99!01604-5# In the last few years it has become possible to build high- mobility heterojunctions with lateral surface superlattices and ''antidot'' arrays. Depending on the strength of the uni- form field and the energy, the system could be considered in the quantum or classical regime, while the strength of the local potential ~magnetic or electrostatic! determines whether the classical trajectories will be regular or chaotic. 1 As the lattice spacing is made much larger than the Fermi wave- length, the electron dynamics reaches a semiclassical regime. In this limit, it turns out that a competition between the clas- sical cyclotron radius and the potential length scale ~the lat- tice period! determines a great deal of the dynamical behav- ior, as we will see below. Given the great flexibility in system fabrication, it is now possible to study the full range of this problem experimentally: from the fully quantum re- gime to the semiclassical mechanics problem. An important example is the dynamics of ballistic electrons in a spatially modulated potential in a magnetic field, and their effect on magnetotransport. 1-3 In the semiclassical regime, commensurability oscillations in the magnetoresistance of modulated two-dimensional electron gases have attracted much attention recently. 1 The commensurability oscillations result from the competition between two length scales: the cyclotron radius Rc5v/v o ~where v is the particle velocity, v o5eBo /mc, and Bo is the applied magnetic field!, and the period of the superstructure a. The case where the potential barriers are defined by an