Flat bands in Weaire-Thorpe model and silicene

TL;DR

This paper applies the Weaire-Thorpe model to silicene, revealing the presence and characteristics of flat bands in its electronic structure, and discusses implications for band engineering and potential magnetic or structural instabilities.

Contribution

The study reformulates the Weaire-Thorpe model using an overlapping molecular-orbital approach to analyze flat bands in silicene, highlighting differences from 3D silicon and implications for material properties.

Findings

Flat bands in silicene are identified and characterized.

Differences between 2D silicene and 3D silicon band structures are elucidated.

Insights into band engineering and potential magnetic or structural instabilities are provided.

Abstract

In order to analytically capture and identify peculiarities in the electronic structure of silicene, Weaire-Thorpe(WT) model, a standard model for treating three-dimensional (3D) silicon, is applied to silicene with the buckled 2D structure. In the original WT model for four hybridized $sp^3$ orbitals on each atom along with inter-atom hopping, the band structure can be systematically examined in 3D, where flat (dispersionless) bands exist as well. For examining silicene, here we re-formulate the WT model in terms of the overlapping molecular-orbital (MO) method which enables us to describe flat bands away from the electron-holesymmetric point. The overlapping MO formalism indeed enables us to reveal an important difference: while in 3D the dipersive bands with cones are sandwiched by doubly-degenerate flat bands, in 2D the dipersive bands with cones are sandwiched by triply-degenerate and non-degenerate (nearly) flat bands, which is consistent with the original band calculation by Takeda and Shiraishi. Thus emerges a picture for why the whole band structure of silicene comprises a pair of dispersive bands with Dirac cones with each of the band touching a nearly flat (narrow) band at $\Gamma$. We can also recognize that, for band engineering, the bonds perpendicular to the atomic plane are crucial, and that a ferromagnetism or structural instabilities are expected if we can shift the chemical potential close to the flat bands.