Evidence of Hofstadter's Fractal Energy Spectrum in the Quantized Hall Conductance

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.