Calculating the polarization in bipartite lattice models: application to an extended Su-Schrieffer-Heeger model

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buir.contributor.authorHetényi, Balázs
buir.contributor.authorPulcu, Yetkin
buir.contributor.authorDoğan, Serkan
buir.contributor.orcidHetényi, Balázs|0000-0002-3680-1147
buir.contributor.orcidPulcu, Yetkin|0000-0001-6029-9217
dc.citation.epage075117-9en_US
dc.citation.issueNumber075117en_US
dc.citation.spage075117-1en_US
dc.citation.volumeNumber103en_US
dc.contributor.authorHetényi, Balázs
dc.contributor.authorPulcu, Yetkin
dc.contributor.authorDoğan, Serkan
dc.date.accessioned2022-02-11T13:40:13Z
dc.date.available2022-02-11T13:40:13Z
dc.date.issued2021-02-08
dc.departmentDepartment of Mathematicsen_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractWe address the question of different representations of Bloch states for lattices with a basis, with a focus on topological systems. The representations differ in the relative phase of the Wannier functions corresponding to the diffferent basis members. We show that the phase can be chosen in such a way that the Wannier functions for the different sites in the basis both become eigenstates of the position operator in a particular band. A key step in showing this is the extension of the Brillouin zone. When the distance between sites within a unit cell is a rational number, p/q, the Brillouin extends by a factor of q. For irrational numbers, the Brillouin zone extends to infinity. In the case of rational distance, p/q, the Berry phase lives on a cyclic curve in the parameter space of the Hamiltonian, on the Brillouin zone extended by a factor of q. For irrational distances, the most stable way to calculate the polarization is to approximate the distance as a rational sequence and use the formulas derived here for rational numbers. The use of different bases are related to unitary transformations of the Hamiltonian, as such, the phase diagrams of topological systems are not altered, but each phase can acquire different topological characteristics when the basis is changed. In the example we use, an extended Su-Schrieffer-Heeger model, the use of the diagonal basis leads to toroidal knots in the Hamiltonian space, whose winding numbers give the polarization.en_US
dc.description.provenanceSubmitted by Burcu Böke (tburcu@bilkent.edu.tr) on 2022-02-11T13:40:13Z No. of bitstreams: 1 Calculating_the_polarization_in_bipartite_lattice_models_Application_to_an_extended_Su-Schrieffer-Heeger_model.pdf: 1564512 bytes, checksum: 4679a6c04135966dc91ea7d8c664874f (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-11T13:40:13Z (GMT). No. of bitstreams: 1 Calculating_the_polarization_in_bipartite_lattice_models_Application_to_an_extended_Su-Schrieffer-Heeger_model.pdf: 1564512 bytes, checksum: 4679a6c04135966dc91ea7d8c664874f (MD5) Previous issue date: 2021-02-08en
dc.identifier.doi10.1103/PhysRevB.103.075117en_US
dc.identifier.eissn075117-1
dc.identifier.issn075117-9
dc.identifier.urihttp://hdl.handle.net/11693/77301
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttps://doi.org/10.1103/PhysRevB.103.075117en_US
dc.source.titlePhysical Review Ben_US
dc.titleCalculating the polarization in bipartite lattice models: application to an extended Su-Schrieffer-Heeger modelen_US
dc.typeArticleen_US

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