Hofstadter butterfly evolution in the space of two-dimensional bravais lattices

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dc.citation.epage063628-11en_US
dc.citation.issueNumber6en_US
dc.citation.spage063628-1en_US
dc.citation.volumeNumber95en_US
dc.contributor.authorYllmaz, F.en_US
dc.contributor.authorOktel, M. Ö.en_US
dc.date.accessioned2018-04-12T11:04:04Z
dc.date.available2018-04-12T11:04:04Z
dc.date.issued2017en_US
dc.departmentDepartment of Physicsen_US
dc.description.abstractThe self-similar energy spectrum of a particle in a periodic potential under a magnetic field, known as the Hofstadter butterfly, is determined by the lattice geometry as well as the external field. Recent realizations of artificial gauge fields and adjustable optical lattices in cold-atom experiments necessitate the consideration of these self-similar spectra for the most general two-dimensional lattice. In a previous work [F. Yllmaz, Phys. Rev. A 91, 063628 (2015)PLRAAN1050-294710.1103/PhysRevA.91.063628], we investigated the evolution of the spectrum for an experimentally realized lattice which was tuned by changing the unit-cell structure but keeping the square Bravais lattice fixed. We now consider all possible Bravais lattices in two dimensions and investigate the structure of the Hofstadter butterfly as the lattice is deformed between lattices with different point-symmetry groups. We model the optical lattice with a sinusoidal real-space potential and obtain the tight-binding model for any lattice geometry by calculating the Wannier functions. We introduce the magnetic field via Peierls substitution and numerically calculate the energy spectrum. The transition between the two most symmetric lattices, i.e., the triangular and the square lattices, displays the importance of bipartite symmetry featuring deformation as well as closing of some of the major energy gaps. The transitions from the square to rectangular lattice and from the triangular to centered rectangular lattices are analyzed in terms of coupling of one-dimensional chains. We calculate the Chern numbers of the major gaps and Chern number transfer between bands during the transitions. We use gap Chern numbers to identify distinct topological regions in the space of Bravais lattices.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T11:04:04Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2017en
dc.identifier.doi10.1103/PhysRevA.95.063628en_US
dc.identifier.issn2469-9926
dc.identifier.urihttp://hdl.handle.net/11693/37146
dc.language.isoEnglishen_US
dc.publisherAmerican Physical Societyen_US
dc.relation.isversionofhttp://dx.doi.org/10.1103/PhysRevA.95.063628en_US
dc.source.titlePhysical Review Aen_US
dc.subjectCrystal latticesen_US
dc.subjectGeometryen_US
dc.subjectMagnetic fieldsen_US
dc.subjectOptical materialsen_US
dc.subjectSpectroscopyen_US
dc.subjectLattice geometryen_US
dc.subjectOne-dimensional chainsen_US
dc.subjectPeriodic potentialsen_US
dc.subjectRectangular latticesen_US
dc.subjectSelf-similar spectraen_US
dc.subjectTight binding modelen_US
dc.subjectTwo-dimensional latticesen_US
dc.subjectWannier functionsen_US
dc.subjectOptical latticesen_US
dc.titleHofstadter butterfly evolution in the space of two-dimensional bravais latticesen_US
dc.typeArticleen_US

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