The size effect and analogous boundary states in a circular non-Hermitian chain

We investigate the size effect and boundary states based on a circular non-Hermitian chain under the nonreciprocal intra-cell coupling and inter-cell coupling regimes. We find that the circular non-Hermitian chain exhibits an even-odd effect of the unit cell corresponding to a large size of the chain, which is different from the open non-Hermitian chain only exhibiting the same effect for a small size of the chain. Moreover, we find that the originally localized bulk states become totally extended via designing the boundary coupling strength appropriately. The extended bulk states reveal the fact of the disappearance of non-Hermitian skin effect. Specially, we show that the circular non-Hermitian chain also possesses the analogous edge states under some parameter regimes, which is pretty counterintuitive since the circular chain usually cannot define a boundary. Our investigations supply the different non-Hermitian phenomena in a circular non-Hermitian chain.