Edge states in a non-Hermitian chiral lattice

Non-Hermiticity can alter the topological properties of energy bands and drive topologically trivial systems with Hermitian limits to generate nontrivial topological edge states. Nevertheless, most efforts were devoted to the study of isotropic systems containing multiple pairs of non-Hermitian components, while the influence of distribution of non-Hermitian components was seldom explored. Here, we first investigated a two-dimensional square-lattice non-Hermitian model in which the losses increase in either clockwise or counterclockwise direction, leading to distinct non-Hermitian chiral structures. The effective Hamiltonian satisfied non-Hermitian particle-hole symmetry, which can induce non-Hermitian zero modes. By combing two chiral structures, various edge states emerged from the interface, whose bands strongly depend on the distribution of non-Hermitian components. And the band properties of edge states were analyzed and predicted basing on the non-Hermitian particle-hole symmetry and hypothetical parity-time symmetry. Furthermore, to validate our theory, we proposed a piezoelectric phononic crystal with an external circuit. The band structures were coincident with our theoretical results. And robust wave propagation was also identified. Our study may provide an alternative method to actively engineer propagating waves in non-Hermitian systems.