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Geometric resonances in the magnetoresistance of hexagonal lateral superlattices

We have measured magnetoresistance of hexagonal lateral superlattices. We observe three types of oscillations engendered by periodic potential modulation having hexagonal-lattice symmetry: amplitude modulation of the Shubnikov-de Haas oscillations, commensurability oscillations, and the geometric resonances of open orbits generated by Bragg reflections. The latter two reveal the presence of two characteristic periodicities, sqrt{3} a / 2 and a / 2, inherent in a hexagonal lattice with the lattice constant a. The formation of the hexagonal-superlattice minibands manifested by the observation of open orbits marks the first step toward realizing massless Dirac fermions in semiconductor 2DEGs.