Effective Hamiltonian for silicene under arbitrary strain from multi-orbital basis

Zhuo Bin Siu,Mansoor B A Jalil

doi:10.1038/s41598-021-86947-z

Abstract

A tight-binding (TB) Hamiltonian is derived for strained silicene from a multi-orbital basis. The derivation is based on the Slater–Koster coupling parameters between different orbitals across the silicene lattice and takes into account arbitrary distortion of the lattice under strain, as well as the first and second-order spin–orbit interactions (SOI). The breaking of the lattice symmetry reveals additional SOI terms which were previously neglected. As an exemplary application, we apply the linearized low-energy TB Hamiltonian to model the current-induced spin accumulation in strained silicene coupled to an in-plane magnetization. The interplay between symmetry-breaking and the additional SOI terms induces an out-of-plane spin accumulation. This spin accumulation remains unbalanced after summing over the Fermi surfaces of the occupied bands and the two valleys, and can thus be utilized for spin torque switching.

Highlights

A tight-binding (TB) Hamiltonian is derived for strained silicene from a multi-orbital basis
We reduce the full four-orbital Hamiltonian to a single-orbital tight-binding Hamiltonian, linearized in k close to the Dirac points, which is useful for subsequent spin accumulation calculations under a small electric field
The breaking of the directional isotropy in strained silicene leads to the emergence of inplane components in the spin–orbit interaction field near the Dirac points and an anisotropic energy dispersion relation in the vicinity of the Dirac points

Summary

Introduction

A tight-binding (TB) Hamiltonian is derived for strained silicene from a multi-orbital basis. Less attention was given on how the resulting bandstructure affects the transport properties of strained silicene In the latter, a convenient method is to consider the linear expansion of the Hamiltonian around the Dirac points and approximate the effects of strain by a single strain-dependent vector gauge potential term[23,38]. A convenient method is to consider the linear expansion of the Hamiltonian around the Dirac points and approximate the effects of strain by a single strain-dependent vector gauge potential term[23,38] Using this approach, Wang et al studied the spin and valley-resolved transmission in a silicene system consisting of a number of alternating strained and unstrained segments subjected to an out-of-plane electric field[39].

Objectives

Conclusion