  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.
