The electronic structure of a quasiperiodic superlattice with slabs of A- and B-type layers is studied within a tight-binding model by use of the transfer matrix and a perturbative approach. It is found that the band gaps vary strongly within the two-dimensional Brillouin zone and, in the case of more than one layer in a slab, there are a few eigenvalues for each ${\mathrm{k}}_{?}$ for which the eigenstates appear to be extended in the quasiperiodic direction. The latter is true even for the Fibonacci chain with more than one atom per cell.

• Received 24 February 1987

DOI:https://doi.org/10.1103/PhysRevLett.59.1476