Feature-rich magneto-electronic properties of bismuthene

Abstract

The generalized tight-binding model, being based on the spin-dependent sublattices, is developed to explore the magnetic quantization of monolayer bismuthene. The sp ^3 orbital hybridizations, site energies, nearest and next-nearest hopping integrals, spin–orbital interactions and magnetic field ( B _z $\hat{z}$ ) are taken into account simultaneously. There exist three groups of low-lying Landau levels (LLs), in which they are mainly from the (6p _x , 6p _y , 6p _z ) orbitals, and only the first group belongs to the unoccupied conduction states. Furthermore, each group is further split into the spin-up- and spin-down-dominated subgroups. The six subgroups present the rich and unique B _z -dependent LL energy spectra, covering the specific or arc-shaped B _z -dependences, the normal/irregular spin–split energies, and the non-crossing/crossing/anti-crossing behaviors. Specially, the second group of valence LLs near the Fermi level can create the frequent inter-subgroup LL anti-crossings since the main and side modes are comparable. The main features of energy spectra can create the special structures in density of states.