Transition Characteristics of Non‐Hermitian Skin Effects in a Zigzag Lattice Without Chiral Symmetry

Abstract

Abstract Non‐Hermitian systems recently have attracted tremendous attention due to their plentiful unique and fascinating properties, among which is the localization of an otherwise extensive bulk eigen‐state at the boundary when the open boundary condition (OBC) is imposed, an interesting phenomenon now referred to as non‐Hermitian skin effect (NHSE). Here, a non‐Hermitian Zigzag lattice model with/without chiral symmetry is investigated with respect to different nearest‐neighbor and long‐range hopping amplitudes and study the transition signature of NHSE by extracting information from the complex eigen‐energy spectra of the system under the periodic boundary condition (PBC), which is verified by the directional inverse participation ratio under OBC. Such an approach provides great simplicity in judging transitions of NHSE especially in lattices without chiral symmetry, where the obtained transition signatures are further confirmed by calculating the topological winding number of the energy under PBC. This work reveals a fundamental way to explore transitions of NHSE, and has a potential in helping understand more other complicated topological physics unique to non‐Hermitian systems.

Keywords

• bulk‐boundary correspondence
• chiral symmetry
• general Brillouin zone
• non‐Hermitian skin effect
• transition point
• zigzag lattices