Topological pumping in an inhomogeneous Aubry–André model

The Aubry–André model is a fundamental theoretical model that exhibits interesting topological features. In this paper, we examine topologically protected boundary states in the inhomogeneous off-diagonal Aubry–André model. In contrast to the homogeneous case, the inhomogeneity triggers boundary states at phase boundaries that separate two distinct non-trivial topological domains. Remarkably, the topological character of the boundary states is predicted through topological pumping, where a boundary state is transferred from one boundary across the bulk region to the other by adiabatically tuning the pump parameter. Moreover, the role of the off-diagonal modulation strength ($\lambda$) on the transfer efficiency of the topological pumping is addressed. To support our results, we investigate the time evolution of a continuous-time quantum walk and show that its spread rate and $\lambda$ are inversely related. Our work provides a new avenue to harness topological features of the Aubry–André model, where topological pumping can be used for robust quantum transport.