Magnetotransport properties of arrays of cross-shaped antidots

In magnetotransport measurements on arrays of cross-shaped antidots, we observe pronounced features in both the longitudinal and transverse magnetoresistivities ${\rho }_{\mathrm{xx}}$ and ${\rho }_{\mathrm{xy}},$ which cannot be understood within the simple framework of commensurability between cyclotron radius and superlattice period. These resonances can be regarded as magnetotransport fingerprints of the complex unit cell. With the help of detailed numerical calculations using classical linear response theory we can ascribe additional maxima in ${\rho }_{\mathrm{xx}}$ to closed orbits in the dotlike potential between four antidots. A pronounced minimum in ${\rho }_{\mathrm{xy}}$ demonstrates the significance of open trajectories.