The energy spectrum of a two-dimensional electron system in a perpendicular homogeneous magnetic field and a weak lateral superlattice potential with square symmetry is composed of Landau bands with recursive internal subband structure. The Hall conductance in the minigaps is anticipated to be quantized in integer multiples of e(2)/h that vary erratically from minigap to minigap in accordance with a Diophantine equation. Hall measurements on samples with the requisite properties uncover this long searched for evidence of Hofstadter's butterflylike energy spectrum.

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Magnetotransport experiments on two-dimensional electron systems with an atomically precise, one-dimensional potential modulation reveal striking quantum interference oscillations. Within a semiclassical framework, they are recognized either as self-interference along closed orbits, many of them rendered possible by magnetic breakdown between Fermi contour segments of the artificial band structure, or as interference-enhanced backscattering. The known commensurability oscillations appear as a special case of the latter mechanism.

We investigated the magnetotransport properties of high mobility InAs/GaSb antidot lattices. In addition to the usual commensurability features at low magnetic fields we found a broad maximum of classical origin around 2.5 T. The latter can be ascribed to a class of rosetta type orbits encircling a single antidot. This is shown by both a simple transport calculation based on a 'classical' Kubo formula and an analysis of the Poincaré surface of section at different magnetic field values. At low temperatures we observe weak 1/B-periodic oscillations superimposed on the classical maximum.

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