Novel Magnetic Quantization of sp$^{3}$ Bonding in Monolayer Tinene

TL;DR

This paper develops a generalized tight-binding model to investigate the magnetic quantization in monolayer tinene, revealing unique Landau level features arising from $sp^{3}$ bonding, spin-orbital coupling, and external fields.

Contribution

It introduces a novel theoretical approach to analyze magnetic quantization in tinene, highlighting effects of $sp^{3}$ bonding and external fields on Landau levels.

Findings

Two groups of low-lying Landau levels with distinct properties

Landau-level splittings induced by electric field and spin-orbital interactions

Unique Landau levels absent in graphene, silicene, and germanene

Abstract

A generalized tight-binding model, which is based on the subenvelope functions of the different sublattices, is developed to explore the novel magnetic quantization in monolayer gray tin. The effects due to the $sp^{3}$ bonding, the spin-orbital coupling, the magnetic field and the electric field are simultaneously taken into consideration. The unique magneto-electronic properties lie in two groups of low-lying Landau levels, with different orbital components, localization centers, state degeneracy, spin configurations, and magnetic- and electric-field dependences. The first and second groups mainly come from the $5p_{z}$ and ($5p_{x}$,$5p_{y}$) orbitals, respectively. Their Landau-level splittings are, respectively, induced by the electric field and spin-orbital interactions. The intragroup anti-crossings are only revealed in the former. The unique tinene Landau levels are absent in graphene, silicene and germanene.