Zak Phase Dislocations in Trimer Lattices
arXiv:2509.15894 · doi:10.3390/sym17101631
Abstract
Wave propagation in periodic media is governed by energy-momentum relation and geometric phases characterizing band topology, such as Zak phase in one-dimensional lattices. We demonstrate that in the off-diagonal trimer lattices Zak phase carries quantized screw-type dislocations winding around degeneracies in parameter space. If the lattice evolves in time periodically, as in adiabatic Thouless pump, corresponding closed trajectory in parameter space is characterized by a Chern number equal the negative total winding number of Zak phase dislocations enclosed by the trajectory. We discuss correspondence between bulk Chern numbers and the edge-states in a finite system evolving along various pumping cycles.
14 pages, 6 figures, to appear in Symmetry (2025)
References in corpus (40)
- Topological Insulators
- Topological insulators and superconductors
- Berry Phase Effects on Electronic Properties
- Topological Photonics
- Topological Photonics
- Photonic Floquet Topological Insulators
- Imaging topological edge states in silicon photonics
- Topological States and Adiabatic Pumping in Quasicrystals
- Direct Measurement of the Zak phase in Topological Bloch Bands
- Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
- A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
- Topological Thouless Pumping of Ultracold Fermions
- Nonlinear topological photonics
- The Zak phase and the existence of edge states in graphene
- Artificial flat band systems: from lattice models to experiments
- Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
- Synthetic Dimension in Photonics
- Light propagation and localization in modulated photonic lattices and waveguides
- Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
- Photonic Topological Insulator in Synthetic Dimensions
- Experimental Observation of Large Chern numbers in Photonic Crystals
- Edge states and topological phases in one-dimensional optical superlattices
- Topological singularities and the general classification of Floquet-Bloch systems
- A single photonic cavity with two independent physical synthetic dimensions
- Active topological photonics
- Nonlinearity-induced photonic topological insulator
- Observation and control of maximal Chern numbers in a chiral topological semimetal
- Topological phases and edge states in a non-Hermitian trimerized optical lattice
- Topological Phase Transitions and Thouless Pumping of Light in Photonic Waveguide Arrays
- Edge states in trimer lattices
- Observation of edge solitons in topological trimer arrays
- One-dimensional topological insulators with noncentered inversion symmetry axis
- Phase spectroscopy of topological invariants in photonic crystals
- Intertwined Topological Phases induced by Emergent Symmetry Protection
- Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
- Universal momentum-to-real-space mapping of topological singularities
- The New Phase due to Symmetry Protected Piecewise Berry Phases; Enhanced Pumping and Non-reciprocity in Trimer Lattices
- Dispersion Suppressed Topological Thouless Pumping
- Non-Hermitian Dirac cones with valley-dependent lifetimes
- Bulk-boundary correspondence in extended trimer Su-Schrieffer-Heeger model