Quantized charge-pumping in higher-order topological insulators

We study the quantized charge pumping of higher-order topological insulators (HOTIs) with edge-corner correspondences based on the combination of the rotation of in-plane magnetic field and the quantum spin Hall effect. A picture of a specific charge pumping process is uncovered with the help of the non-equilibrium Green's function method. Significantly, we demonstrate that the quantized charge pumping current is achieved without the participation of bulk states, and the charges move along the boundary of the sample. Furthermore, the effects of external parameters on the pumping current is also studied. We find that the magnitude and direction of the pumping current can be manipulated by adjusting the coupling strength between the leads and sample. Our work deepens the understanding of the charge pumping in HOTIs and extends the study of their transport properties.