Diamagnetism of quasicrystals due to Bragg's reflexions

We point out that in quasicrystals, one has to take into account a large but finite number of effective Bragg's reflexions out of the dense set. This leads to small gaps on the Fermi surface (some tenths of meV), much narrower than the usual Hume-Rothery one's (0.2-0.5 eV) invoked for explaining their stability. Small pockets of electrons and holes with very anisotropic effective masses are thus existing. The very low effective masses in some directions for electron pockets are responsible for the diamagnetism of quasicrystals. As these gaps are very sensitive to impurities, phasons, so is the diamagnetism. (C) 1997 Elsevier Science Ltd.