Generalized Hofstadter model on a cubic optical lattice: From nodal bands to the three-dimensional quantum Hall effect

Abstract

We propose that a tunable generalized three-dimensional Hofstadter Hamiltonian can be realized by engineering the Raman-assisted hopping of ultracold atoms in a cubic optical lattice. The Hamiltonian describes a periodic lattice system under artificial magnetic fluxes in three dimensions. For certain hopping configurations, the bulk bands can have Weyl points and nodal loops, respectively, allowing the study of both the two nodal semimetal states within this system. Furthermore, we illustrate that with proper rational fluxes and hopping parameters, the system can exhibit the three-dimensional quantum Hall effect when the Fermi level lies in the band gaps, which is topologically characterized by one or two nonzero Chern numbers. Our proposed optical-lattice system provides a promising platform for exploring various exotic topological phases in three dimensions.

10 pages, 5 figures

References in corpus (17)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
• Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
• Line of Dirac Nodes in Hyper-Honeycomb Lattices
• Spin Hall effects for cold atoms in a light induced gauge potential
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
• Probing non-Abelian statistics of Majorana fermions in ultracold atomic superfluid
• Theory of the Three Dimensional Quantum Hall Effect in Graphite
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Relativistic quantum effects of Dirac particles simulated by ultracold atoms
• Type-II Weyl Points in Three-Dimensional Cold Atom Optical Lattices
• Direct Probe of Topological Order for Cold Atoms
• Realising Type II Weyl Points in an Optical Lattice

Cited by in corpus (8)

• Topological quantum matter with cold atoms
• Realistic Floquet semimetal with exotic topological linkages between arbitrarily many nodal loops
• Emergent pseudospin-1 Maxwell fermions with a threefold degeneracy in optical lattices
• Floquet engineering and simulating exceptional rings with a quantum spin system
• Exploring topological double-Weyl semimetals with cold atoms in optical lattices
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Transition from nodal loop to nodal chain phase in a periodically modulated optical lattice
• On the algebraic area of cubic lattice walks