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arXiv · 2509.15894

Zak Phase Dislocations in Trimer Lattices

Tileubek Uakhitov·Abdybek Urmanov·Serik E. Kumekov·Anton S. Desyatnikov
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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.

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Tileubek Uakhitov, Abdybek Urmanov, Serik E. Kumekov, Anton S. Desyatnikov. 2025-09-19. Zak Phase Dislocations in Trimer Lattices. https://doi.org/10.3390/sym17101631

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