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      Evolution of the Hofstadter butterfly in a tunable optical lattice

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      Author
      Yllmaz, F.
      Ünal, F. N.
      Oktel, M. O.
      Date
      2015
      Source Title
      Physical Review A
      Print ISSN
      2469-9926
      Electronic ISSN
      2469-9934
      Publisher
      American Physical Society
      Volume
      91
      Issue
      6
      Pages
      063628-10 - 063628-1
      Language
      English
      Type
      Article
      Item Usage Stats
      143
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      101
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      Abstract
      Recent 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.
      Keywords
      Crystal lattices
      Geometry
      Honeycomb structures
      Magnetic fields
      Optical materials
      Topology
      Applied magnetic fields
      Checkerboard lattices
      Honeycomb lattices
      Real space structure
      Self-similar fractals
      Topological equivalence
      Topological properties
      Zero magnetic fields
      Optical lattices
      Permalink
      http://hdl.handle.net/11693/21669
      Published Version (Please cite this version)
      http://dx.doi.org/10.1103/PhysRevA.91.063628
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      • Department of Physics 2299
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