Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice

Abstract

The stability of $\nu =1/3$ Fractional Chern Insulator (FCI) phase is analysed on the example of checkerboard lattice undergoing a transition into Lieb lattice. The transition is performed by the addition of a second sublattice, whose coupling to the checkerboard sites is controlled by sublattice staggered potential. We investigate the influence of these sites on the many body energy gap between three lowest energy states and the fourth state. We consider cases with different complex phases acquired in hopping and a model with a flattened topologically nontrivial band. We find that an interaction with the additional sites either open the single-particle gap or enlarge the existing one, which translates into similar effect on the many-particle gap. Evidences of FCI phase for a region in a parameter space with larger energy gap are shown by looking at momenta of the three-fold degenerate ground state, spectral flow, and quasihole excitation spectrum.

7 pages, 7 figures

References in corpus (19)

• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Experimental realisation of the topological Haldane model
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• 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
• Topological flat band models with arbitrary Chern numbers
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Non-Abelian topological insulators from an array of quantum wires
• Fractional (Chern and topological) insulators
• Enhancing the stability of a fractional Chern insulator against competing phases
• Quantum Anomalous Hall Effect in Flat Band Ferromagnet
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Quantum phases of disordered flatband lattice fractional quantum Hall systems
• Magnetic translation algebra with or without magnetic field in the continuum or on arbitrary Bravais lattices in any dimension

Cited by in corpus (13)

• Experimental realization and characterization of an electronic Lieb lattice
• Floquet topological phase transition in $\alpha$-${\mathcal{T}}_3$ lattice
• Desiging Artificial Lieb Lattice on Metal Surface
• Designer Flat Bands in Quasi-One-Dimensional Atomic Lattices
• Wigner crystallization in topological flat bands
• Experimental Realization of Two-Dimensional Buckled Lieb lattice
• Flat band transport and Josephson effect through a finite-size sawtooth lattice
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice
• Holstein polaron in a pseudospin-$1$ quantum spin Hall system: first and second order topological phase transitions
• Ground state spin and excitation energies in half-filled Lieb lattices
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems