Non-Hermitian Thouless pumping: Interplay between topological charge pumping and directional tunneling

Motivated by experimental realizations of the lattice models with directional tunneling and the generalized bulk-edge correspondence brought by a similarity transformation, we study the topological charge pumping using the Rice-Mele (RM) model with directional tunneling (also termed as the non-Hermitian RM model). In momentum space, through a similaritylike transformation, we map the non-Hermitian RM model to a Hermitian one. Under the biorthogonal basis, the pumping is dictated by a Chern number of the Hermitian RM model. This can be verified by experiments where both the non-Hermitian RM model and its Hermitian conjugation are realized. Under the right-right vector basis, which is relevant to experiments where only the non-Hermitian one is required, we find that the charge pumping contains a dynamical and a topological part. To reveal the topological contribution, an experimental scheme of canceling the dynamical term is proposed.