Dimerization, Trimerization and Quantum pumping

TL;DR

This paper explores one-dimensional topological models with dimerization and trimerization, demonstrating their edge states, analyzing their mechanisms, and constructing quantum pumping processes linked to topological properties, with implications for experiments.

Contribution

It systematically connects topological models with quantum pumping and provides insights for experimental realization in optical lattices and photonic quasicrystals.

Findings

Edge states appear in dimerized and trimerized models.

Quantum pumping is demonstrated with a charge transfer per cycle.

Pumping is linked to nonzero Chern number and gapless states.

Abstract

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the appearance of edge states and the mechanism of dimerization and trimerization is analyzed. Then we show that a quantum pumping process can be constructed based on each one-dimensional topological model. The quantum pumping process is explicitly demonstrated by the instantaneous energy spectrum and local current. The result shows that the pumping is assisted by the gapless states connecting the bands and one charge is pumped during a cycle, which also defines a nonzero Chern number. Our study systematically shows the connection of one-dimensional topological models and quantum pumping, and is useful for the experimental studies on topological phases in optical lattices and photonic quasicrystals.