Bloch-like Electronic Wave Functions in Two-Dimensional Quasicrystals

Electrons in quasicrystals generically possess critical wave functions that are neither exponentially-localized nor extended, but rather decay algebraically in space. Nevertheless, motivated by recent calculations on the square and cubic Fibonacci quasicrystals, we investigate whether it is possible to obtain extended wave functions expressed as linear combinations of degenerate, or nearly-degenerate, critical eigenfunctions. We find that not only is this possible, but that the wave functions that emerge are Bloch-like, exhibiting the quasiperiodic long-range order of the underlying quasicrystal. We discuss the significance of this result for the study of electronic properties of real quasicrystals.