Characterizing the Hofstadter butterfly's outline with Chern numbers
arXiv:0808.1440 · doi:10.1088/0953-4075/42/5/055302
Abstract
In this work, we report original properties inherent to independent particles subjected to a magnetic field by emphasizing the existence of regular structures in the energy spectrum's outline. We show that this fractal curve, the well-known Hofstadter butterfly's outline, is associated to a specific sequence of Chern numbers that correspond to the quantized transverse conductivity. Indeed the topological invariant that characterizes the fundamental energy band depicts successive stairways as the magnetic flux varies. Moreover each stairway is shown to be labeled by another Chern number which measures the charge transported under displacement of the periodic potential. We put forward the universal character of these properties by comparing the results obtained for the square and the honeycomb geometries.
arXiv commentAccepted for publication in J. Phys. B (Jan 2009)
References in corpus (21)
- Many-Body Physics with Ultracold Gases
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
- Unconventional Integer Quantum Hall effect in graphene
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Fractional quantum Hall states of atoms in optical Lattices
- New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials
- Bose-Einstein Condensates with Large Number of Vortices
- High field fractional quantum Hall effect in optical lattices
- Bose-Einstein Condensates in Rotating Lattices
- Optical lattice quantum Hall effect
- Mean-field theory for Bose-Hubbard Model under a magnetic field
- Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
- Hall effects in Bose-Einstein condensates in a rotating optical lattice
- Fully Frustrated Cold Atoms
- Hall conductance of Bloch electrons in a magnetic field
- Vortex lattices of bosons in deep rotating optical lattices
- Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
- Phonon-induced artificial magnetic fields
- Spatial patterns in optical lattices submitted to gauge potentials
- Mott-Insulator Transition for Ultracold Fermions in Two-Dimensional Optical Lattices
Cited by in corpus (17)
- Ultracold atomic gas in non-Abelian "magnetic" fields: the quantum Hall effect supremacy
- Ultracold atomic gases in non-Abelian gauge potentials: The case of constant Wilson loop
- Fractional Quantum Hall Physics in Jaynes-Cummings-Hubbard Lattices
- Universality of Hofstadter butterflies on hyperbolic lattices
- Topological multi-mode waveguide QED
- Floquet engineering to exotic topological phases in systems of cold atoms
- Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
- Spin-valley system in a gated MoS-monolayer quantum dot
- Butterfly Floquet Spectrum in Driven SU(2) Systems
- Anomalous charge pumping in a one-dimensional optical superlattice
- Magnonic Floquet Hofstadter Butterfly
- Berry curvature effects in the Bloch oscillations of a quantum particle under a strong (synthetic) magnetic field
- Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems
- Driven Hofstadter Butterflies and Related Topological Invariants
- Translational symmetry breaking and the disintegration of the Hofstadter butterfly
- Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
- Polarization as a topological quantum number in graphene