Evolution of the Hofstadter butterfly in a tunable optical lattice
Author
Yllmaz, F.
Ünal, F. N.
Oktel, M. O.
Date
2015Source 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
ArticleItem Usage Stats
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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 latticesGeometry
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/11693/21669Published Version (Please cite this version)
http://dx.doi.org/10.1103/PhysRevA.91.063628Collections
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