Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices

Abstract

We identify the existence of various symmetry-protected topological states in one-dimensional superlattices with periodically modulated hopping amplitudes or on-site potentials, which can be characterized by the quantized Berry phase $\pi$ or the emergence of a pair of degenerate boundary states. It is shown that there may exist three types of topological phases, which are protected by the inversion symmetry, the chiral symmetry, and both of them, respectively, depending on the modulations, the odd or even modulation period. The connection between the hopping and potential modulations is also discussed. Furthermore, we demonstrate that the topological phase protected by the inversion symmetry can be realized in the interacting boson systems trapped in the same superlattices. The results are very possibly studied experimentally in the superlattice systems engineered with state-of-art technologies.

arXiv comment5 pages, 3 figures; Supplement material added (2 pages, 3 figures). To appear in Phys. Rev. B Rapid Communication

References in corpus (41)

• Berry Phase Effects on Electronic Properties
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Topological States and Adiabatic Pumping in Quasicrystals
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• The effects of interactions on the topological classification of free fermion systems
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Inversion Symmetric Topological Insulators
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Edge states and topological phases in one-dimensional optical superlattices
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Topological phases of generalized Su-Schrieffer-Heeger models
• Topological orbital ladders
• Transition from fractional to Majorana fermions in Rashba nanowires
• Manipulating Topological Edge Spins in One-Dimensional Optical Lattice
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• Exact diagonalization: the Bose-Hubbard model as an example
• Symmetry protected topological phases in non-interacting fermion systems
• Simulating Z_2 topological insulators with cold atoms in a one-dimensional optical lattice
• Topological Bose-Mott Insulators in a One-Dimensional Optical Superlattice
• AIII and BDI Topological Systems at Strong Disorder
• Radiative topological states in resonant photonic crystals
• Characterization of a topological Mott insulator in one dimension
• Exact Study of the 1D Boson Hubbard Model with a Superlattice Potential
• Topological equivalence of crystal and quasicrystal band structures
• From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model
• Topological phase in one-dimensional interacting fermion system
• Interaction effects on 1D fermionic symmetry protected topological phases
• Fractional topological states of dipolar fermions in one-dimensional optical superlattices
• Fractional topological phase in one-dimensional flatbands with nontrivial topology
• Topological transitions of interacting bosons in one-dimensional bi-chromatic optical lattices
• Topological Mott insulators of ultracold atomic mixtures induced by interactions in one-dimensional optical superlattices
• Hard-core bosons in one-dimensional interacting topological bands

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• Quantum walks in commensurate off-diagonal Aubry-André-Harper model
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• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings
• Robust one-dimensionality at twin-grain-boundaries in MoSe${}_2$
• Topologically nontrivial states in one-dimensional nonlinear bichromatic superlattices
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
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