Absence of non-Hermitian skin effect in a one-dimensional lattice with nontrivial spectral topology

Recent studies introducing non-Hermitian parameters to topological lattices revealed the breakdown of bulk-boundary correspondence, which is attributed to the non-Hermitian skin effect. In such systems, the system's spectrum under a periodic boundary condition (PBC) never matches the spectrum under an open boundary condition (OBC), and the OBC eigenmodes forming the continuum bands are skin modes localized at a boundary instead of bulk modes extending across the lattice. For one-dimensional lattices, theoretical studies revealed an elegant relation between the nontrivial PBC spectral topology and the emergence of non-Hermitian skin effects under OBC. In this talk, we will present a case that falls outside this prediction, that is, the PBC spectrum has a nontrivial spectral topology, but the non-Hermitian skin effect is absent, and all modes are extended bulk modes under OBC. The system is a unidirectionally coupled double-chain lattice, with one chain being Hermitian, and the other being non-Hermitian. We show that the existence and absence of the non-Hermitian skin effect can lead to rich and unique wavepacket dynamics. The phenomenon can be explained by observing the properties of the invariant subspaces in the Hamiltonian. Our findings deepen and enrich the understanding of non-Hermitian skin effect and show new possibilities in non-Hermitian skin dynamics.