Quasicrystals as alloys with short-range order

The electronic structure of quasiperiodic lattices is studied. An alloy theory, including short-range order effects, is used to approximate Fibonacci and Thue-Morse lattices. Short-range order is treated by embedding small clusters in an alloy that itself incorporates a two-site approximation, and the probabilities of these clusters are used to construct an efficient procedure for the calculation of electronic properties. This approach allows easy identification of the contributions of particular clusters to the electronic density of states. As the short-range order is increased via the number of clusters, the density of states can be clearly seen to transition from that of an alloy to that of a quasicrystal. It is shown that the techniques may be applied to other lattices defined by substitution rules.