Spatially separated skin effect and edge states in one-dimensional semi–Su-Schrieffer-Heeger lattices

We investigate the skin effect and topological properties in the one-dimensional semi--Su-Schrieffer-Heeger (semi--SSH) lattice, in which the intersite couplings in one direction are uniform but in the other direction the intersite couplings change alternately. Following the detailed theoretical demonstration, we find that in this system, the skin effect can be tunable by adjusting the magnitudes of the intersite couplings in the two directions. However, the change of the skin effect does not necessarily modulate the topological edge states, and such two phenomena are allowed to appear in a spatially separated way. Therefore, we propose one scheme to change the directionality of the topological edge states and the localized bulk states, by controlling the intersite couplings. This promotes the understanding of the skin effects and topological properties in the one-dimensional SSH lattices with nonreciprocal couplings.