Strictly localized states in the octagonal Ammann-Beenker quasicrystal

Simple item page
buir.contributor.authorOktel, Mehmet Özgür
buir.contributor.orcidOktel, Mehmet Özgür|0000-0001-8921-8388
dc.citation.epage014204-18en_US
dc.citation.issueNumber014204en_US
dc.citation.spage014204-1en_US
dc.citation.volumeNumber104en_US
dc.contributor.authorOktel, Mehmet Özgür
dc.date.accessioned2022-02-14T10:48:23Z
dc.date.available2022-02-14T10:48:23Z
dc.date.issued2021-07-06
dc.departmentDepartment of Physicsen_US
dc.description.abstractAmmann-Beenker lattice is a two-dimensional quasicrystal with eightfold symmetry, which can be described as a projection of a cut from a four-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and investigate the strictly localized states at the center of the spectrum. We use a numerical method based on the generation of finite lattices around a given perpendicular space point and QR decomposition of the Hamiltonian to count the strictly localized states. We apply this method to count the frequency of localized states in lattices of up to 100 000 sites. We obtain an orthogonal set of compact localized states by diagonalizing the position operator projected onto the manifold spanned by the zero-energy states. We identify 20 localized state types and calculate their exact frequencies through their perpendicular space images. Unlike the Penrose lattice, all the localized state types are eightfold symmetric around an eight edge vertex, and all vertex types can support localized states. The total frequency of these 20 types gives a lower bound of fLS=30796−21776√2≃0.08547 for the fraction of strictly localized states in the spectrum. This value is in agreement with the numerical calculation and very close to the recently conjectured exact fraction of localized states fEx=3/2−√2≃0.08579.en_US
dc.identifier.doi10.1103/PhysRevB.104.014204en_US
dc.identifier.eissn1550-235X
dc.identifier.issn1098-0121
dc.identifier.urihttp://hdl.handle.net/11693/77322
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://doi.org/10.1103/PhysRevB.104.014204en_US
dc.source.titlePhysical Review B (Condensed Matter and Materials Physics)en_US
dc.subjectLocalizationen_US
dc.subjectQuasicrystalsen_US
dc.subjectTight-binding modelen_US
dc.titleStrictly localized states in the octagonal Ammann-Beenker quasicrystalen_US
dc.typeArticleen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Strictly_localized_states_in_the_octagonal_Ammann-Beenker_quasicrystal.pdf
Size:
4.61 MB
Format:
Adobe Portable Document Format
Description:
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.69 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Department of Physics