Spin- and Valley-Dependent Electronic Structure in Silicene Under Periodic Potentials

Yun-Fang Li,Wei-Tao Lu,Hong-Yu Tian

doi:10.1186/s11671-018-2495-4

Abstract

We study the spin- and valley-dependent energy band and transport property of silicene under a periodic potential, where both spin and valley degeneracies are lifted. It is found that the Dirac point, miniband, band gap, anisotropic velocity, and conductance strongly depend on the spin and valley indices. The extra Dirac points appear as the voltage potential increases, the critical values of which are different for electron with different spins and valleys. Interestingly, the velocity is greatly suppressed due to the electric field and exchange field, other than the gapless graphene. It is possible to achieve an excellent collimation effect for a specific spin near a specific valley. The spin- and valley-dependent band structure can be used to adjust the transport, and perfect transmissions are observed at Dirac points. Therefore, a remarkable spin and valley polarization is achieved which can be switched effectively by the structural parameters. Importantly, the spin and valley polarizations are greatly enhanced by the disorder of the periodic potential.

Highlights

Two-dimensional (2D) Dirac materials with hexagonal lattice structures are being explored extensively since the discovery of graphene, such as silicene [1, 2], transition metal dichalcogenides [3, 4], and phosphorene [5]
We found that the spin and valley indices have different impacts on the extra Dirac points and anisotropic velocity which can be tuned by the structural parameters
As U increases, extra Dirac points appear, the number of which increases in the meantime

Summary

Introduction

Two-dimensional (2D) Dirac materials with hexagonal lattice structures are being explored extensively since the discovery of graphene, such as silicene [1, 2], transition metal dichalcogenides [3, 4], and phosphorene [5]. Graphene has many particular properties, its application is limited by the zero band gap and the weak spin-orbit interaction (SOI). Graphene and silicene have similar band structures around K and K valleys, and the low energy spectra of both are described by the relativistic Dirac equation [13]. Silicene has a strong intrinsic SOI and a buckled structure. The strong SOI could open a gap at Dirac points [13, 14] and lead to a coupling between the spin and valley degrees of freedom. The buckled structure allows us to control the band gap by an external electric field perpendicular to the silicene sheet [14–16]. Silicene has the advantage that it is more compatible with existing

Methods

Results

Conclusion