Conductivity in quasicrystals via hierarchically variable-range hopping.

Abstract

This paper takes the structure example of the AlPdMn quasicrystal, as determined from diffraction data, to derive useful self-similarity rules in consistency with composition and atomic valence constraints. These rules are then accounted for to explain inelastic-neutron-scattering data and thermal conductivity behavior. Basically, three regimes can be identified: extended low-energy phonon conductivity at low temperature following roughly a ${\mathit{T}}^{2}$ power law which transforms into a plateau of constant conductivity and, at higher temperature, a phonon assisted localized-state hopping mechanism with a ${\mathit{T}}^{3/2}$ power law and hierarchically distributed hopping distances. Electrical conductivity is also briefly analyzed along the same approach: accordingly, pure perfect quasicrystals should show a \ensuremath{\sigma}(T)\ensuremath{\propto}T behavior with deviation in ${\mathit{T}}^{0.5}$ at low temperature and in ${\mathit{T}}^{3/2}$ at high temperature coming from quasiperiodicity breaking. \textcopyright{} 1996 The American Physical Society.