Novel Magnetic Quantization of Bismuthene

TL;DR

This paper develops a generalized tight-binding model to analyze the magnetic quantization and Landau level structures in monolayer bismuthene, revealing complex spin-dependent energy spectra and unique magnetic field behaviors.

Contribution

It introduces a comprehensive model incorporating orbital hybridizations, spin interactions, and magnetic effects to explore Landau levels in bismuthene, highlighting novel spectral features.

Findings

Identification of three groups of Landau levels mainly from 6p orbitals.

Observation of complex Bz-dependent energy spectra with crossing and anti-crossing behaviors.

Detection of special density of states structures due to Landau level features.

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.