A Selection of Surveys. K F Kelton, P C Gibbons, A I Goldman, J. Non-Cryst. S Takeuchi and T Fujiwara, World Scientific Research Topics in Quasicrystals. Quasicrystals differ from crystals in the variety and frequency distributions of local environments. One must compute the electron system to obtain the stability of the atomic order in a quasicrystal.
Electrons occupy the one-electron levels but obey fermion properties.
Attempts of electron computations in quasicrystals use band theory in a periodic approximant scheme, in particular the LMTO method based on atomic orbitals. In quasicrystals a search for a pseudogap at the Fermi energy is suggested as a reason of stability and low conductivity. It provides a criticism of band methods for quasicrystals. The interpretation and verification of the computed density of states is doubtful, there are too many narrow bands. New algebraic recursive methods are suggested.