Perpendicular space accounting of localized states in a quasicrystal

buir.contributor.authorMirzhalilov, Murod
buir.contributor.authorOktel, Mehmet Özgür
dc.citation.epage064213-17en_US
dc.citation.issueNumber6en_US
dc.citation.spage064213-1en_US
dc.citation.volumeNumber102en_US
dc.contributor.authorMirzhalilov, Murod
dc.contributor.authorOktel, Mehmet Özgür
dc.date.accessioned2021-03-02T09:03:58Z
dc.date.available2021-03-02T09:03:58Z
dc.date.issued2020
dc.departmentDepartment of Physicsen_US
dc.description.abstractQuasicrystals can be described as projections of sections of higher dimensional periodic lattices into real space. The image of the lattice points in the projected-out dimensions, called the perpendicular space, carries valuable information about the local structure of the real space lattice. In this paper, we use perpendicular space projections to analyze the elementary excitations of a quasicrystal. In particular, we consider the vertex tight-binding model on the two-dimensional Penrose lattice and investigate the properties of strictly localized states using their perpendicular space images. Our method reproduces the previously reported frequencies for the six types of localized states in this model. We also calculate the overlaps between different localized states and show that the number of type-five and type-six localized states which are independent from the four other types is a factor of golden ratio τ=(1+√5)/2 higher than previously reported values. Two orientations of the same type-five or type-six which are supported around the same site are shown to be linearly dependent with the addition of other types. We also show through exhaustion of all lattice sites in perpendicular space that any point in the Penrose lattice is either in the support of at least one localized state or is forbidden by local geometry to host a strictly localized state.en_US
dc.identifier.doi10.1103/PhysRevB.102.064213en_US
dc.identifier.issn2469-9950
dc.identifier.urihttp://hdl.handle.net/11693/75696
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://dx.doi.org/10.1103/PhysRevB.102.064213en_US
dc.source.titlePhysical Review Ben_US
dc.subjectQuasicrystalsen_US
dc.subjectTight-binding modelen_US
dc.subjectCrystalline systemsen_US
dc.titlePerpendicular space accounting of localized states in a quasicrystalen_US
dc.typeArticleen_US

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