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dc.contributor.authorYllmaz F.en_US
dc.contributor.authorÜnal F.N.en_US
dc.contributor.authorOktel, M.O.en_US
dc.date.accessioned2016-02-08T09:49:32Z
dc.date.available2016-02-08T09:49:32Z
dc.date.issued2015en_US
dc.identifier.issn10502947en_US
dc.identifier.urihttp://hdl.handle.net/11693/21669
dc.description.abstractRecent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically nontrivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend sensitively on the geometry of the underlying lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature (London) 483, 302 (2012)NATUAS0028-083610.1038/nature10871] presents a unique opportunity to study this dependence. In this paper, we calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard lattice to the honeycomb lattice, two square-lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly. This merging is topologically nontrivial, as it is accomplished by sequential closings of gaps. Ensuing Chern number transfer between the bands can be probed with the adjustable lattice experiments. We also calculate the Chern numbers of the gaps for qualitatively different spectra and discuss the evolution of topological properties with underlying lattice geometry. © 2015 American Physical Society.en_US
dc.language.isoEnglishen_US
dc.source.titlePhysical Review A - Atomic, Molecular, and Optical Physicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevA.91.063628en_US
dc.subjectCrystal latticesen_US
dc.subjectGeometryen_US
dc.subjectHoneycomb structuresen_US
dc.subjectMagnetic fieldsen_US
dc.subjectOptical materialsen_US
dc.subjectTopologyen_US
dc.subjectApplied magnetic fieldsen_US
dc.subjectCheckerboard latticesen_US
dc.subjectHoneycomb latticesen_US
dc.subjectReal space structureen_US
dc.subjectSelf-similar fractalsen_US
dc.subjectTopological equivalenceen_US
dc.subjectTopological propertiesen_US
dc.subjectZero magnetic fieldsen_US
dc.subjectOptical latticesen_US
dc.titleEvolution of the Hofstadter butterfly in a tunable optical latticeen_US
dc.typeArticleen_US
dc.departmentDepartment of Physics
dc.citation.volumeNumber91en_US
dc.citation.issueNumber6en_US
dc.identifier.doi10.1103/PhysRevA.91.063628en_US
dc.publisherAmerican Physical Societyen_US


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