Charge pumping in one dimensional quasicrystals characterized by Bott index

In recent years, topological phases in quasiperiodic systems attract much attention. In these systems, we cannot use conventional methods defined in the momentum space for lack of periodicity. Hence, topological numbers in the quasiperiodic systems are calculated from the real space,.
In this talk, we will talk about the charge pumping in the quasiperiodic systems by applying Bott index that computes topological indices based on real space formulation. While we can use Bott index directly for topological numbers defined in two dimensional space, it is necessary to modify Bott index for the application to charge pumping as the pumping parameter behaves like a momentum.