Zak-Phase Dislocations in Trimer Lattices

Wave propagation in periodic media is governed by energy–momentum relations 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 pumps, the corresponding closed trajectory in parameter space is characterized by a Chern number equal to the negative total winding number of Zak phase dislocations enclosed by the trajectory. We discuss the correspondence between bulk Chern numbers and the edge states in a finite system evolving along various pumping cycles.