Topological quantized edge-pumping-spin flip in Rice-Mele model with spin-orbit coupling

TL;DR

This paper explores how spin-orbit coupling in a spinful Rice-Mele model leads to topological spin pumping, with quantized edge spin flips serving as a dynamic signature of the boundary-bulk correspondence.

Contribution

It demonstrates that spin-orbit coupling transforms a degeneracy point into a loop, enabling quantized edge spin flips and revealing a novel dynamic boundary-bulk correspondence in the model.

Findings

Quantized spin pumping occurs when enclosing the nodal loop.

Edge spin flips are quantized and observable after double periods.

The boundary-bulk correspondence is demonstrated dynamically.

Abstract

The quantized Thouless pumping charge in a spinless Rice-Mele (RM) model originates from a degeneracy point in the parameter space and cannot be detected when open boundary conditions are applied. In this work, we investigate the topological features of a spinful Rice-Mele (RM) model. We demonstrate that spin-orbit coupling facilitates the transition of a single degenerate point into a degenerate loop, which is anticipated to be the source of the topological characteristics. When periodic boundary conditions are considered, we find that the pumping spin is zero for an adiabatic loop within the nodal loop and is 2 (in units of $\hbar /2$) for an adiabatic passage enclosing the nodal loop. When open boundary conditions are considered, the boundary-bulk correspondence is demonstrated by quantized pumping-spin flips at the edges, which can be obtained by completing double periods of a closed passage, rather than a single cycle. Our findings reveal an alternative dynamic manifestation of the boundary-bulk correspondence.