Topological transitions in a model with Particle-Hole symmetry, Pancharatnam-Berry Curvature and Dirac Points

Abstract

We study the topology and geometry of a fermionic model on the honeycomb lattice with spin-dependent hopping which breaks the time-reversal and charge-conjugation symmetries but preserves their composition. We show that in such a case the Zak phases are topological invariants that characterize the semi-metallic state at half-filling and determine the edge state structure. As the strength of the spin-dependent hopping varies, the model shows several Lifshitz transitions corresponding to creation and merging of multiple Dirac points. We discuss the possible realization of this model in cold atom systems and propose experimental signals of detecting the Dirac points and Pancharathnam-Berry curvature of the bands.

13 pages, 17 figures; movies at http://www.youtube.com/playlist?list=PLINihIBfmWkB6h86e8URUdTbdxemY83Vc

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• Classification of topological insulators and superconductors in three spatial dimensions
• Merging of Dirac points in a two-dimensional crystal
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
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• Optical Flux Lattices for Ultracold Atomic Gases
• Bloch-Zener oscillations
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Cited by in corpus (6)

• (3+1)-dimensional topological quantum field theory from a tight-binding model of interacting spinless fermions
• Distinct-symmetry spin liquid states and phase diagram of Kitaev-Hubbard model
• Topological multiferroic phases in the extended Kane-Mele-Hubbard Model in the Hofstadter regime
• Quantum geometry of correlated many-body states
• Dirac points merging and wandering in a model Chern insulator
• Spin-resolved Mott crossover and entanglement in the half-filled Hubbard model