Landau subbands generated by a lateral electrostatic superlattice - chasing the Hofstadter butterfly

Abstract

Magnetoresistance studies on two-dimensional electron systems in GaAs - AlGaAs heterojunctions exposed to voltage-tunable square lateral superlattices with periods in the 100 nm range reveal at low temperatures a characteristic splitting of individual Landau bands. Around magnetic field values at which p/q flux quanta penetrate the unit cell of the superlattice, with p and q being small integers, p subbands can be observed. A discussion of which conditions have to be met to reveal such Hofstadter-type splitting of Landau bands illuminates the experimental difficulties that have to be overcome in chasing the Hofstadter butterfly.