Edge Charge Pumping in Insulators with Inversion Symmetry*

Higher order topological insulators were first proposed to host half quantized corner charge associated with degenerate corner states. Such proposal has motivated wide interest in predicting the corner charge in various situations and its relation to the electric multipole moment. In this talk, we will discuss the change of the corner charge for noninteracting two dimensional insulators with inversion symmetry undergoing adiabatic evolution. We show that the change of the corner charge is accounted for by the adiabatic current flowing along the edges of the system. To derive the analytical expression for the adiabatic current, the study of systems with quasi-1D geometry is necessary, indicating that the change of the corner charge is neither a purely bulk nor edge effect, but rather a mixed one. The derived adiabatic current was examined and shows good agreement with the numerical calculation of Benalcazar-Bernevig-Hughes model. Our work suggests that the study of the change of corner charge and the associated adiabatic edge current may advance the understanding of electric multipole moment in crystalline insulators.