Floquet Engineering of Haldane Chern Insulators and Chiral bosonic phase transitions
arXiv:1608.00025 · doi:10.1103/PhysRevB.95.045102
Abstract
The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band structure associated with chiral edge modes (without the presence of a net unit flux in a unit cell), then referring to the quantum anomalous Hall effect. Focusing on (interacting) boson systems in s-wave bands of the lattice, we show how to engineer through the Floquet theory, a quantum phase transition between a uniform superfluid and a BEC (Bose-Einstein Condensate) analog of FFLO (Fulde-Ferrell-Larkin-Ovchinnikov) states, where bosons condense at non-zero wave-vectors. We perform a Ginzburg-Landau analysis of the quantum phase transition on the graphene lattice, and compute observables such as chiral currents and the momentum distribution. The results are supported by exact diagonalization calculations and compared with those of the isotropic situation. The validity of high-frequency expansion in the Floquet theory is also tested using time-dependent simulations for various parameters of the model. Last, we show that the anisotropic choice for the effective vector potential allows a bosonization approach in equivalent ladder (strip) geometries.
24 pages, 16 figures, minor modifications and references added
References in corpus (33)
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Topological Photonics
- Quantum fluids of light
- Photovoltaic Hall effect in graphene
- Analogs of quantum Hall effect edge states in photonic crystals
- Topological characterization of periodically-driven quantum systems
- The Magnus expansion and some of its applications
- Observation of Superfluidity of Polaritons in Semiconductor Microcavities
- Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
- Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
- Bose-Einstein condensation of photons in an optical microcavity
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- Tunable gauge potential for neutral and spinless particles in driven lattices
- Many-body localization in periodically driven systems
- Time-reversal symmetry breaking in circuit-QED based photon lattices
- Orbital superfluidity in the -band of a bipartite optical square lattice
- Multi-Component Quantum Gases in Spin-Dependent Hexagonal Lattices
- Dispersive regime of circuit QED: photon-dependent qubit dephasing and relaxation rates
- Tuning laser-induced bandgaps in graphene
- State preparation and dynamics of ultracold atoms in higher lattice orbitals
- Topological index for periodically driven time-reversal invariant 2D systems
- Periodically-driven quantum matter: the case of resonant modulations
- Vortex and Meissner phases of strongly-interacting bosons on a two-leg ladder
- Radiation effects on the electronic structure of bilayer graphene
- Scattering Theory for Floquet-Bloch States
- Time independent description of rapidly oscillating potentials
- Anomalous Hall Effects of Light and Chiral Edge Modes on the Kagome Lattice
- Chiral Mott Insulators, Meissner Effect, and Laughlin States in Quantum Ladders
- Non-equilibrium phase transition in a periodically driven XY spin chain
- Condensed Groundstates of Frustrated Bose-Hubbard Models
- Mott transition in a two-leg Bose-Hubbard ladder under an artificial magnetic field
- Avoided level crossing spectroscopy with dressed matter waves
- Chiral Bosonic Phases on the Haldane Honeycomb Lattice