• About
  • Policies
  • What is open access
  • Library
  • Contact
Advanced search
      View Item 
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Physics
      • View Item
      •   BUIR Home
      • Scholarly Publications
      • Faculty of Science
      • Department of Physics
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Strictly localized states on the Socolar dodecagonal lattice

      Thumbnail
      View / Download
      5.7 Mb
      Author(s)
      Keskiner, Mehmet Akif
      Oktel, Mehmet Özgür
      Date
      2022-08-22
      Source Title
      Physical Review B
      Print ISSN
      2469-9950
      Electronic ISSN
      2469-9969
      Publisher
      American Physical Society
      Volume
      106
      Issue
      6
      Pages
      064207-1 - 064207-18
      Language
      English
      Type
      Article
      Item Usage Stats
      6
      views
      1
      downloads
      Abstract
      Socolar dodecagonal lattice is a quasicrystal closely related to the better-known Ammann-Beenker and Penrose lattices. The cut and project method generates this twelvefold rotationally symmetric lattice from the six-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and use the acceptance domains of the vertices in perpendicular space to count the frequency of strictly localized states. We numerically find that these states span fNum 7.61% of the Hilbert space. We give 18 independent localized state types and calculate their frequencies. These localized state types provide a lower bound of fLS = 10919−6304√3 2 0.075854, accounting for more than 99% of the zero-energy manifold. Numerical evidence points to larger localized state types with smaller frequencies, similar to the Ammann-Beenker lattice. On the other hand, we find sites forbidden by local connectivity to host localized states. Forbidden sites do not exist for the Ammann-Beenker lattice but are common in the Penrose lattice. We find a lower bound of fForbid 0.038955 for the frequency of forbidden sites. Finally, all the localized state types we find can be chosen to have constant density and alternating signs over their support, another feature shared with the Ammann-Beenker lattice.
      Permalink
      http://hdl.handle.net/11693/111308
      Published Version (Please cite this version)
      https://www.doi.org/10.1103/PhysRevB.106.064207
      Collections
      • Department of Physics 2550
      Show full item record

      Browse

      All of BUIRCommunities & CollectionsTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCoursesThis CollectionTitlesAuthorsAdvisorsBy Issue DateKeywordsTypeDepartmentsCourses

      My Account

      Login

      Statistics

      View Usage StatisticsView Google Analytics Statistics

      Bilkent University

      If you have trouble accessing this page and need to request an alternate format, contact the site administrator. Phone: (312) 290 2976
      © Bilkent University - Library IT

      Contact Us | Send Feedback | Off-Campus Access | Admin | Privacy