Hofstadter butterfly of a quasicrystal
  The energy spectrum of a tight-binding Hamiltonian is studied for the two-dimensional quasiperiodic Rauzy tiling in a perpendicular magnetic field. This spectrum known as a Hofstadter butterfly displays a very rich pattern of bulk gaps that are labeled by four integers, instead of two for periodic systems. The role of phason-flip disorder is also investigated in order to extract genuinely quasiperiodic properties. This geometric disorder is found to only preserve main quantum Hall gaps. 
J.-N Fuchs, J. Vidal
cond-mat.mes-hall cond-mat.other