Eur. Phys. J. Plus (2022) 137: 133
https://doi.org/10.1140/epjp/s13360-022-02370-x

Regular Article

Band structures of the bowtie lattice and its ribbons influenced by -symmetric imaginary potentials

¹ College of Sciences, Northeastern University, 110819, Shenyang, China
² State Key Laboratory of Rolling and Automation, Northeastern University, 110819, Shenyang, China

^c zhanglianlian@mail.neu.edu.cn

Received: 12 March 2020
Accepted: 10 January 2022
Published online: 18 January 2022

Abstract

By introducing the -symmetric complex potentials, we investigate the properties of the band structure of the bowtie lattice with symmetry. It is found that the complex potentials directly lead to the enhancement of the energy-band overlap, including the occurrence of the threefold degeneracy. Meanwhile, the flat band is destroyed gradually and the -symmetry breaking occurs. When the two-dimensional lattice is cut into one-dimensional ribbons, the effect of the complex potentials is tightly dependent on the types of the ribbon edges, i.e., zigzag or armchair. For the case of armchair ribbon, the roles of the -symmetric potentials are more dependent on its width. We believe that this work is useful for understanding the band structures of the -symmetric bowtie-lattice systems.