Adiabatic charge pumping, rice-mele model

Abstract

We apply the Berry phase and the Chern number to show that the periodically and slowly changing the parameters of a one-dimensional solid, it is possible to pump particles in it. The number of particles (charge) pumped is an integer per cycle, that is given by a Chern number. Along the way we will introduce important concepts of edge state branches of the dispersion relation, and bulk–boundary correspondence. Since we are working towards understanding time-independent topological insulators, this chapter might seem like a detour. However, bulk–boundary correspondence of 2-dimensional Chern insulators, at the heart of the theory of topological insulators, is best understood via a mapping to an adiabatic charge pump. The concrete system we use in this chapter is the simplest adiabatic charge pump, obtained by adding staggered onsite potential to the SSH model. It is known as the Rice-Mele (RM) model.