ABSTRACT
As noted in Chapter 1, Section 1.2, Traverse et al. [2] in 1988 revealed from the soft x-ray emission spectra a large depression in the DOS at the Fermi level in the Al-Mn quasicrystal relative to its amorphous and crystalline counterparts. ἀ eir pioneering work already hinted at the presence of a pseudogap in quasicrystals. At that time, however, people had intuitively expected that first-principles band calculations were beyond a practical level of computations, even for 1/1-1/1-1/1 approximants. A breakthrough was brought about by Fujiwara in 1989 [3], who performed LMTO-ASA band calculations for the Al-Mn approximant, containing some 138 atoms in the unit cell. ἀ is work revealed a deep pseudogap at the Fermi level and suggested it to be most likely responsible for the stability of such CMAs containing icosahedral clusters similar to those in quasicrystals. Since then, first-principles LMTO-ASA electronic structure calculations have been extensively carried out to affirm whether a pseudogap is a universal feature of all approximants and whether it becomes more pronounced, as the order of the approximants is increased toward that of a quasicrystal. Readers may consult the recent developments on this topic in books and in review articles [4-6].
