Coexistence of topological edge states and skin effects in the non-Hermitian Su-Schrieffer-Heeger model with long-range nonreciprocal hopping in topoelectric realizations

Recently, the topological phase in non-Hermitian systems has been a rapidly expanding field. The iconic features of non-Hermitian systems are exceptional points at which the eigenmodes coalesce and the non-Hermitian skin effect. We study the non-Hermitian Su-Schrieffer-Heeger model with long-range nonreciprocal hopping and find the model exhibiting topologically nontrivial phases which can be characterized by the non-Bloch winding number. With specific parameter values, the skin effect can be eliminated. As long-range nonreciprocal hopping is not easy for experimental implementations, we furthermore propose a feasible electrical-circuit simulation with operational amplifiers to implement the non-Hermitian term to realize these interesting states.