8- Pmmn borophene: edge states in competition with Landau levels and local vacancy states

The tight-binding method is used to investigate the electronic and magnetic properties of borophene nano-ribbons (BNRs) in the presence of a perpendicular magnetic field. Most BNRs exhibit metallic characteristics due to edge bands. Additionally, the appearance of Landau levels (LLs) is strongly influenced by the edge states, contrasting with the sheet platform which produces distinct LLs. We also investigated single atomic vacancy disorders in BNRs and observed localized vacancy states (LVSs) resulting from atomic disorder. Both LVSs and LLs are influenced by the edge states, underscoring that the electronic and magnetic properties of BNRs are strongly edge-dependent. This aspect is crucial for consideration in experimental, theoretical, and computational studies.