Unconventional Hybridization of Skin Modes in Coupled non-Hermitian Chains

Non-Hermitian systems exhibit a plethora of unusual topological phenomena including the extreme eigenstate localization of eigenstates, known as the non-Hermitian skin effect (NHSE), which occurs under open boundary conditions (OBC). Here, we report on the eigenstate localization in a system of two coupled non-Hermitian chains with dissimilar inverse skin lengths in which the NHSE can be switched on or off by modulating the inter-chain coupling strength. In the limit of small inter-chain strength, the NHSE is present at both ends of the coupled system because of the weak hybridization between the eigenstates of the individual chains. The eigenspectrum under OBC exhibits a discontinuous jump known as the critical NHSE (CNHSE) as the chain length increases. However, when the inter-chain coupling strength and hence the hybridization between eigenstates becomes significant, the CNHSE vanishes and the eigenstates are no longer all localized at the same boundary. Instead, a peculiar “half-half skin localization” occurs in composite chains with opposite signs of inverse skin lengths, where half of the eigenstates are exponentially localized at one chain and the remainder of the eigenstates on the other chain. Our results provide new theoretical insights into the critical non-Hermitian phenomena in coupled systems.