Nonreciprocal Su-Schrieffer-Heeger lattice in the presence of next-nearest-neighboring coupling

Abstract

We pay attention to the band structure of the nonreciprocal Su-Schrieffer-Heeger (SSH) lattice modified by next-nearest-neighboring (NNN) coupling. It is found that the NNN coupling induces the chiral symmetry by breaking the particle-hole symmetry, leading to the energies of the end modes in the topologically-nontrivial region dependent on the structural parameters. Also, with the increase of NNN coupling, the encounter of the bulk bands modifies the phase transition manner in a new way. The other phenomenon lies in that the localization of the end modes and the non-Hermitian skin effect can be modulated efficiently by the interplay between the NNN and nonreciprocal couplings. Based on these results, one can understand the nontrivial role of NNN coupling in modifying the energy bands and topological properties of the nonreciprocal SSH lattice.