Exploring Thouless Pumping in the Generalized Creutz Model: A Graphical Method and Modulation Schemes

TL;DR

This paper introduces a graphical method to analyze topological phases in Thouless pumping within a generalized Creutz model, demonstrating practical modulation schemes and quantized matter wave transport in one-dimensional lattice systems.

Contribution

It presents a novel graphical representation for topological phases and explores various modulation schemes in a generalized Creutz model for Thouless pumping.

Findings

Graphical depiction of topological phases linked to Chern and Zak phases.

Identification of linking number patterns related to topological invariants.

Demonstration of quantized charge pumping in the generalized Creutz model.

Abstract

Thouless pumping with nontrivial topological phases provides a powerful means for the manipulation of matter waves in one-dimensional lattice systems. The band topology is revealed by the quantization of pumped charge. In the context of Thouless pumping, we present a graphical representation for the topological phases characterized by the Chern number of an effective two-dimensional band. We illustrate how the two topological phases with distinct Zak phase is connected in the pumping process. Such a visual depiction exhibits typical patterns that is directly related to a linking number and to the Chern number, allowing for the construction of Thouless pumping schemes in a practical way. As a demonstration, we present a generalized Creutz model with tunable Peierls phase, inter-leg imbalance and diagonal hopping. Various modulation schemes for Thouless pumping are studied, focusing on their graphical representations in Bloch space, as well as the quantized pumping phenomenon in real space.