Stability of classical electron orbits in triangular electron billiards

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Abstract
Using a triangular electron billiard, we investigate in detail which electron trajectories lead to the commensurability effects observed in the magnetoresistance. By comparing the magnetoresistance with simulations of classical electron trajectories, we are able to correlate the maxima of the resistance with specific electron trajectories. The findings are supported by a comparison with data obtained from other devices with different geometries. An explanation why certain trajectories are more important for the resistance than others is obtained from a numerical stability analysis using classical chaos theory. Short trajectories that have a small Liapunov exponent are most important for the resistance. Application of a bias voltage has a strong effect on the magnetoresistance. Here we suggest that voltage-induced small-angle electron-electron scattering acts like a small perturbation of the electron motion, to which chaotic trajectories are most sensitive.