Spin-orbital coupling induced isolated flat band in bismuthene with <b>k</b>-dependent spin texture

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.