Quantum Chaos in Magnetic Band Structures

Abstract

Magnetic band structures of an antidot superlattice in a perpendicular magnetic field are analysed with respect to signatures of quantum chaos. For an integer number of magnetic flux quanta threading a unit cell, they show up in the distribution of nearest-neighbour level spacings and the spectral rigidity. As the unique property of this infinite system, we find in a single magnetic band structure coexistence of spectra belonging to different universality classes depending on the magnetic wave vector. For a rational number of flux quanta the universal features of quantum chaos disappear with increasing flux denominator and level clustering occurs in the spectrum although classical motion is widely chaotic.