Quantum spin-valley Hall effect in AB-stacked bilayer silicene

Kyu Won Lee,Cheol Eui Lee

doi:10.1038/s41598-019-55927-9

Abstract

Our density functional theory calculations show that while AB-stacked bilayer silicene has a non-quantized spin-valley Chern number, there exist backscattering-free gapless edge states within the bulk gap, leading to a quantum spin-valley Hall effect. Using a tight-binding model for a honeycomb bilayer, we found that the interlayer potential difference and the staggered AB-sublattice potential lead to abrupt and gradual change of the valley Chern number from a quantized value to zero, respectively, while maintaining backscattering-free gapless edge states if the valley Chern number is not too close to zero. Under an inversion symmetry-breaking potential in the form of the staggered AB-sublattice potential, such as an antiferromagnetic order and a hexagonal diatomic sheet, a finite but non-quantized (spin-)valley Chern number can correspond to a quantum (spin-)valley Hall insulator.

Highlights

Silicene, one of the two-dimensional group IV materials such as graphene, is a single layer of silicon atoms arranged in a honeycomb lattice and is similar to a buckled graphene lattice[1,2,3,4]
If the inversion symmetry-breaking potential increases, the Berry curvature peak pertaining to each valley can be broadened and partially mixed with each other, and the valley Chern number obtained by integrating the the Berry curvature around a valley will deviate from the quantized value
Our density functional theory (DFT) calculations show that while the intralayer ferrimagnetic and interlayer antiferromagnetic order of AB-stacked bilayer silicene gives a non-quantized spin-valley Chern number, there exist backscattering-free gapless edge states corresponding to a quantum spin-valley Hall effect

Summary

Introduction

One of the two-dimensional group IV materials such as graphene, is a single layer of silicon atoms arranged in a honeycomb lattice and is similar to a buckled graphene lattice[1,2,3,4]. Our density functional theory (DFT) calculations show that while the intralayer ferrimagnetic and interlayer antiferromagnetic order of AB-stacked bilayer silicene gives a non-quantized spin-valley Chern number, there exist backscattering-free gapless edge states corresponding to a quantum spin-valley Hall effect. Chern number from a quantized value, while maintaining backscattering-free gapless edge states corresponding to a quantum valley Hall effect.

Results

Conclusion