Topological properties and skin effects modulated by different-density nonreciprocal couplings in the Su-Schrieffer-Heeger structure

Abstract

We pay attention to the topological properties and skin effects in the one-dimensional Su-Schrieffer-Heeger (SSH) structure, by considering the presence of different-density non-reciprocal couplings. We find that when only one single non-reciprocal coupling term is introduced, e.g., in the middle of the SSH structure, edge states can be induced around the sites suffering from the non-reciprocal coupling. As one non-reciprocal coupling term is introduced in each two cells, the topological phase transition is modified. Besides, new topological edge states and skin effects appear at the ends of the SSH structure, and the edge states can be differentiated by their localities, localization degrees, and the imaginary part of energy. Furthermore, if two neighboring cells of the SSH structure are coupled by the non-reciprocal coupling, the topological edge states and skin effect more well-defined, accompanied by the further change of the topological phase transition condition. These results suggest that the non-reciprocal coupling plays a unique and important role in modulating the topological properties and the skin effects of the one-dimensional SSH structure.