Spin-orbital coupling induced isolated flat band in bismuthene with <b>k</b> -dependent spin texture
Shifang Li, Xizhi Shi, Jin Li, Chaoyu He, Tao Ouyang, Chao Tang, Jianxin Zhong
Abstract
Flat bands exhibit many exotic physical phenomena due to the dispersionless features and are receiving widespread attentions. In this work, a metastable bismuthene allotrope (P-3m1-$\mathrm{B}{\mathrm{i}}_{72}$) with isolated flat bands near the Fermi level was identified, through high-throughput tight-binding calculations, from more than 500 allotropes. P-3m1-$\mathrm{B}{\mathrm{i}}_{72}$ features the kagome characteristic of an interlaced distribution of triangles and hexagons. First-principles calculations revealed that this structure is a dynamically stable phase of bismuthene and energetically more favorable than many previously predicted bismuthene allotropes. Based on the high-level functional of HSE06 (HSE stands for Heyd-Scuseria-Ernzerhof), three isolated flat bands are confirmed in the band structures of P-3m1-$\mathrm{B}{\mathrm{i}}_{72}$, located in the vicinity of the Fermi level. These isolated flat bands originate from the kagome-like features of the atomic configuration as well as the charge distributions, and their isolation and flatness are severely affected by the strength of spin-orbital coupling (SOC). Additionally, the spin textures of flat bands in P-3m1-$\mathrm{B}{\mathrm{i}}_{72}$ are k dependent and exhibit twofold rotation symmetry in reciprocal space. Our work provides a candidate material for studying the properties of isolated flat bands in a strong SOC system.