2020/12/29 by Anuradha Jagannathan · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Anderson localization #Boundary value problem #Combinatorics #Condensed matter physics #Fibonacci number #Materials science #Mathematics #Nanocluster Synthesis and Applications #Periodic boundary conditions #Phason #Physics #Quantum mechanics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Range (aeronautics) #Scale (ratio) #Scale invariance #Statistical physics #Theoretical physics #Translational symmetry #X-ray Diffraction in Crystallography #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/revmodphys.93.045001
Revised reformatted version with new figures (48 pages, 45 figures) to be published in Reviews of Modern Physics
openalex publication_date 2020/12/29 · arxiv created 2021/08/26 · openalex created_date 2021/11/22 · arxiv updated 2021/11/24 · openalex updated_date 2026/08/05
The distinctive electronic properties of quasicrystals stem from their long range structural order, with invariance under rotations and under discrete scale change, but without translational invariance. d-dimensional quasicrystals can be described in terms of lattices of higher dimension D>d, and many of their properties can be simply derived from analyses that take into account the extra "hidden" dimensions. In particular, as recent theoretical and experimental studies have shown, quasicrystals can have topological properties inherited from the parent crystals. These properties are discussed here for the simplest of quasicrystals, the 1D Fibonacci chain. The Fibonacci noninteracting tight-binding Hamiltonians are characterized by multifractality of spectrum and states, which is manifested in many of its physical properties, notably in transport. Perturbations due to disorder and re-entrance phenomena are described, along with the crossover to strong Anderson localization. Perturbations due to boundary conditions also give information on the spatial and topological electronic properties, as is shown for the superconducting proximity effect. Related models including phonon and mixed Fibonacci models are discussed, as well as generalizations to other quasiperiodic chains and higher dimensional extensions. Interacting quasiperiodic systems and the case for many body localization are briefly discussed. Some experimental realizations of the 1D quasicrystal and their potential applications are described.