Negative magnetoresistance due to ballistic weak localization in a dense hexagonal lattice of antidots

Abstract

An experimental analysis of the negative magnetoresistance due to weak localization in a dense hexagonal lattice of antidots created from a two-dimensional electron gas formed at an AlGaAs/GaAs heterojunction is presented. The low-field magnetoresistance is perfectly described by the conventional theory for disordered conductors, using the phase coherence length ${l}_{\ensuremath{\varphi}}$ and a B-independent prefactor \ensuremath{\alpha} as adjustable parameters. An unusual ${T}^{\ensuremath{-}1/4}$ dependence is found for ${l}_{\ensuremath{\varphi}},$ which is in contradiction to the predictions of most of the models proposed for phase breaking processes. A saturation of ${l}_{\ensuremath{\varphi}}$ is observed below 600 mK. Surprisingly, \ensuremath{\alpha}, which determines the amplitude of the weak localization correction to the conductivity, exhibits high values (1.56), and a behavior that cannot be explained by current theories of weak localization in disordered conductors nor in ballistic systems. We explain semiclassically our results in terms of electrons trapped in the unit cells formed by the neighboring antidots, such that the length of the interfering paths is limited by the geometry of the cell. In this case, the weak localization and negative magnetoresistance are more likely to be determined by a specific dimension of the system rather than any decoherence process.