Quasicrystals bands

Abstract. We compute the velocity correlation function of electronic states close to the Fermi energy, in approximants of quasicrystals. As we show the long time value of this correlation function is small. This means a small Fermi velocity, in agreement with previous band structure studies. Furthermore the correlation function is negative on a large time interval which means a phenomenon of backscattering. As shown in previous studies the backscattering can explain unusual conduction properties, observed in these alloys, such as for example the increase of conductivity with disorder. 

M.A. Kaliteevski, S. Brand, R.A. Abram, T.E. Krauss, R. De La Rue, P. Millar, Two-dimensional Penrose-tiled photonic quasicrystals from diffraction pattern to band structure. Nanotechnology 11, 274 (2000)... 

A quasicrystal is a quasiperiodic structure that is ordered but aperiodic, i.e., it lacks translational order. Its unit cell has defined angles and distances with respect to other unit cells but long-range translational order is missing. In addition to intriguing structural characteristics, the transport properties of quasicrystals are expected to be unique due to the missing translational order. For example, Man et al. showed that photonic quasicrystals are excellent candidates for photonic band gap materials, where the existence of photonic waves is forbidden in photonic band gap ranges [35]. 

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