Flat bands and nontrivial topological properties in an extended Lieb lattice
arXiv:1912.12308 · doi:10.1103/PhysRevB.100.235145
Abstract
We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing topologically nontrivial phases when intrinsic spin-orbit (ISO) coupling is introduced in the microscopic description of the corresponding tight-binding Hamiltonian of the system. This ISO coupling strength acts like a complex next-nearest-neighbor hopping term for this model and can be, in principle, tuned in a real-life experimental setup. In the presence of this ISO coupling, the band spectrum of the system gets gapped out, leading to nonzero integer values of the spin Chern number for different bands, indicating the nontrivial topological properties of the system. Furthermore, we show that for certain values of the ISO coupling, nearly flat bands with nonzero Chern numbers emerge in this lattice model. This opens up the possibility of realizing interesting fractional quantum spin Hall physics in this model when interaction is taken into account. This study might be very useful in an analogous optical lattice experimental setup. A possible application of our results can also be anticipated in the field of photonics using single-mode photonic waveguide networks.
9 pages, 9 figures, accepted for publication in PRB
References in corpus (29)
- Many-Body Physics with Ultracold Gases
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
- High temperature fractional quantum Hall states
- Fractional quantum Hall states at zero magnetic field
- Nearly-flat bands with nontrivial topology
- Observation of a localized flat-band state in a photonic Lieb lattice
- Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
- Observation of bound states in Lieb photonic lattices
- Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing
- Anyons and the quantum Hall effect - a pedagogical review
- Realistic Time-Reversal Invariant Topological Insulators With Neutral Atoms
- Engineering Time-Reversal Invariant Topological Insulators With Ultra-Cold Atoms
- Topological Insulators on the Lieb and Perovskite Lattices
- Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
- Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
- Flat Bands Under Correlated Perturbations
- Detecting Chiral Edge States in the Hofstadter Optical Lattice
- Anderson localisation in tight-binding models with flat bands
- Chiral Flat Bands: Existence, Engineering and Stability
- Realizing and Detecting the Haldane's Quantum Hall effect with Ultracold Atoms
- Aharonov-Bohm photonic cages in waveguide and coupled resonator lattices by synthetic magnetic fields
- Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
- Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
- Effects of Smooth Boundaries on Topological Edge Modes in Optical Lattices
- Topological flat Wannier-Stark bands
- Quantum localized states in photonic flat-band lattices
- Quantum anomalous Hall effect on star lattice with spin-orbit coupling and exchange field
- Flux modulated flat band engineering in square-kagome ladder network
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- General construction of flat bands with and without band crossings based on wave function singularity
- Localized dynamics arising from multiple flat bands in a decorated photonic Lieb lattice
- Magnetism and topological phases in an interacting decorated honeycomb lattice with spin-orbit coupling
- Molecular dipoles in designer honeycomb lattices
- RKKY couplings in the Lieb lattice: flat-band induced frustration