  The non-Hermitian skin effect (NHSE) in non-Hermitian lattice systems depicts
the exponential localization of eigenstates at system's boundaries. It has led
to a number of counter-intuitive phenomena and challenged our understanding of
bulk-boundary correspondence in topological systems. This work aims to
investigate how the NHSE localization and topological localization of in-gap
edge states compete with each other, with several representative static and
periodically driven 1D models, whose topological properties are protected by
different symmetries. The emerging insight is that at critical system
parameters, even topologically protected edge states can be perfectly
delocalized. In particular, it is discovered that this intriguing
delocalization occurs if the real spectrum of the system's edge states falls on
the same system's complex spectral loop obtained under the periodic boundary
condition. We have also performed sample numerical simulation to show that such
delocalized topological edge states can be safely reconstructed from
time-evolving states. Possible applications of delocalized topological edge
states are also briefly discussed.
