Rich Magnetic Quantization Phenomena in AA Bilayer Silicene

Po-Hsin Shih,Thi-Nga Do,Danhong Huang,Godfrey Gumbs,Hai Duong Pham,Ming-Fa Lin

doi:10.1038/s41598-019-50704-0

Abstract

The rich magneto-electronic properties of AA-bottom-top (bt) bilayer silicene are investigated using a generalized tight-binding model. The electronic structure exhibits two pairs of oscillatory energy bands for which the lowest conduction and highest valence states of the low-lying pair are shifted away from the K point. The quantized Landau levels (LLs) are classified into various separated groups by the localization behaviors of their spatial distributions. The LLs in the vicinity of the Fermi energy do not present simple wave function modes. This behavior is quite different from other two-dimensional systems. The geometry symmetry, intralayer and interlayer atomic interactions, and the effect of a perpendicular magnetic field are responsible for the peculiar LL energy spectra in AA-bt bilayer silicene. This work provides a better understanding of the diverse magnetic quantization phenomena in 2D condensed-matter materials.

Highlights

Silicene, an isostructure to graphene, is purely made of silicon atoms through both the sp[2] and sp[3] bondings
The stable and non-stable electronic valleys are formed from the electronic states near the high-symmetry points of the hexagonal first Brillouin zone
There exist the M, K and Γ valleys with different conduction and valence band-edge state energies of about (0.5 eV, −0.51 eV), (1.19 eV, −1.21 eV), and (1.43 eV, −1.50 eV), respectively. These special valleys are expected to be closely related to the magnetic quantizations of the initial Landau levels, as discussed later

Summary

Introduction

An isostructure to graphene, is purely made of silicon atoms through both the sp[2] and sp[3] bondings. Theoretical investigations have been focused on the fundamental properties of monolayer and bilayer silicene with or without adatom chemisorptions or guest atom substitutions based on various approaches, covering the first-principles calculations[8,9,10,11,12,13,14,15,16], the generalized tight-binding model[17,18], and the effective-mass approximation[19]. The interplay between intrinsic interactions and electric or magnetic fields may cause the destruction of (z = 0)-plane mirror symmetry (electric field) and the appearance of periodic Peierls phases (magnetic field), respectively The former gives rise to the spin-dominated split energy band and the significant change in band gap[19] the latter yields highly degenerate Landau levels[17]. For bilayer silicene, phenomenological models might not be suitable for solving the magnetic-field-dominated fundamental properties due to significant buckling, the largely enhanced spin-orbital interactions and the complex interlayer hopping integrals. The free carrier densities are expected to be quite sensitive to buckling and stacking configurations

Methods

Results

Conclusion