Evolution of the Hofstadter butterfly in a tunable optical lattice
| Autor: | Mehmet Oktel, F. Nur Ünal, Fırat Yılmaz |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
High Energy Physics::Lattice
Lattice field theory Applied magnetic fields FOS: Physical sciences Geometry Crystal lattices Checkerboard lattices Zero magnetic fields Topology Real space structure Particle in a one-dimensional lattice Topological properties Quantum mechanics Lattice (order) Lattice plane Self-similar fractals Physics Optical lattice Topological equivalence Empty lattice approximation Atomic and Molecular Physics and Optics Honeycomb lattices Reciprocal lattice Quantum Gases (cond-mat.quant-gas) Optical lattices Magnetic fields Optical materials Honeycomb structures Condensed Matter - Quantum Gases Lattice model (physics) |
| Zdroj: | Physical Review A |
| ISSN: | 1094-1622 1050-2947 0028-0836 |
| DOI: | 10.1103/physreva.91.063628 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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