Magnetic quantization in monolayer bismuthene

The magnetic quantization in monolayer bismuthene is investigated by the generalized tight-binding model. The quite large Hamiltonian matrix is built from the tight-binding functions of the various sublattices, atomic orbitals and spin states. Due to the strong spin orbital coupling and sp$^{\mathrm{3}}$ bonding, monolayer bismuthene has the diverse low-lying energy bands such as the parabolic, linear and oscillating energy bands. The main features of band structures are further reflected in the rich magnetic quantization. Under a uniform perpendicular magnetic field (B$_{\mathrm{z}})$, three groups of Landau levels (LLs) with distinct features are revealed near the Fermi level. Their B$_{\mathrm{z}}$-dependent energy spectra display the linear, square-root and non-monotonous dependences, respectively. These LLs are dominated by the combinations of the 6p$_{\mathrm{z}}$ orbital and (6p$_{\mathrm{x}}$,6p$_{\mathrm{y}})$ orbitals as a result of strong sp$^{\mathrm{3}}$ bonding. Specifically, the LL anti-crossings only occur between LLs originating from the oscillating energy band.