Summary
From rigorous mathematical developments to extensive numerical calculations in realistic models of periodic approximants or 3D quasiperiodic systems, anomalous diffusion has been clearly connected either with quasiperiodic correlations, or with geometrical and chemical features of realistic models in which atomic species and their local environment have been shown to be fundamental.
Criticality in 1D quasiperiodic systems is related to algebraic localization of the eigenstates, singular continuous spectra, and peculiar transport scaling of the conductance. In higher dimension, an analytical analysis of critical states turned out to be rather difficult, but systematic numerical calculations gradually gives a better understanding of this kind of localization due to quasiperiodic order. On the other hand, periodic approximants give an accurate description of the geometrical local environments that electrons may encounter while propagating. They also may conserve, to some extent, the peculiar order-induces-quantum interference leading to localization. Electron-electron interactions may play an important role in i-phases of AlPdRe. It is suggested that a Coulomb gap may occur as a consequence of the quasiperiodic potential.
Keywords
- Anomalous Diffusion
- High Structural Quality
- Singular Continuous Spectrum
- Periodic Approximants
- Fibonacci Chain
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Roche, S., Berger, C., Mayou, D. (2002). Electronic Conductivity of Quasicrystals and Approximants. In: Suck, JB., Schreiber, M., Häussler, P. (eds) Quasicrystals. Springer Series in Materials Science, vol 55. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05028-6_16
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