Localization and topological transitions in generalized non-Hermitian SSH models

We study the localization and topological transitions of the generalized non-Hermitian SSH models, where the non-Hermiticities are introduced by the complex quasiperiodic hopping and the nonreciprocal hopping. We elucidate the universality of the models and how many models can be mapped to them. Under the open boundary condition, two delocalization transitions are found due to the competition between the Anderson localization and the boundary localization from the nontrivial edge states and the non-Hermitian skin effect. Under the periodic boundary condition, only one delocalization transition is found due to the disappearance of the non-Hermitian skin effect. The winding numbers of energy and the Lyapunov exponents in analytical form are obtained to exactly characterize the two deloaclizateon transitions. It finds that the delocalization transitions don't accompany the topological transition. Furthermore, the large on-site non-Hermiticity and the large nonreciprocal hopping are all detrimental to the topological transitions. However, the large nonreciprocal hopping enhances the Anderson localizations. The above analyses are verified by calculating the energy gap and the inverse of the participation ratio numerically.