Hofstadter butterfly evolution in the space of two-dimensional bravais lattices
Oktel, M. Ö.
Physical Review A
American Physical Society
063628-1 - 063628-11
Item Usage Stats
MetadataShow full item record
The 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.
Tight binding model
Published Version (Please cite this version)http://dx.doi.org/10.1103/PhysRevA.95.063628
Showing items related by title, author, creator and subject.
Pairing and vortex lattices for interacting fermions in optical lattices with a large magnetic field Zhai, H.; Umucalılar, R. O.; Oktel, M. Ö. (The American Physical Society, 2010)We study the structure of a pairing order parameter for spin-1/2 fermions with attractive interactions in a square lattice under a uniform magnetic field. Because the magnetic translation symmetry gives a unique degeneracy ...
Xianlong, G.; Polini, M.; Tosi, M. P.; Tanatar, Bilal (World Scientific Publishing Co., 2008)Interacting two-component Fermi gases loaded in a one-dimensional (1D) lattice and subjected to a harmonic trapping potential exhibit interesting compound phases in which fluid regions coexist with local Mott-insulator ...
Ghazanfari, N.; Keles, A.; Oktel, M. O. (American Physical Society, 2014-02-21)We consider a rapidly rotating two-component Bose-Einstein condensate with short-range s-wave interactions as well as dipolar coupling. We calculate the phase diagram of vortex lattice structures as a function of the ...