Spin-valley splitting of electron beam in graphene

Yu Song,Lei Xie,Shun Li,Jian Zhang,Zhi-Gui Shi

doi:10.1063/1.4968180

Abstract

We study spatial separation of the four degenerate spin-valley components of an electron beam in a EuO-induced and top-gated ferromagnetic/pristine/strained graphene structure. We show that, in a full resonant tunneling regime for all beam components, the formation of standing waves can lead sudden phase jumps ∼−π and giant lateral Goos-Hänchen shifts as large as the transverse beam width, while the interplay of the spin and valley imaginary wave vectors in the modulated regions can lead differences of resonant angles for the four spin-valley flavors, manifesting a spin-valley beam splitting effect. The splitting effect is found to be controllable by the gating and strain.

Highlights

The fourfold spin-valley degenerate degrees of freedom in bulk graphene can support rich physics and novel applications associated with multicomponent quantum Hall effects[1,2,3] and linear conductance filtering.[4,5,6,7]
For the spin-valley quantum Hall effects, it is experimentally demonstrated that, the approximate SU(4) isospin symmetry of Landau levels (LL) in graphene can be broken by interactions such as strong Coulomb interaction, Zeeman effect, and lattice scale interactions, manifesting as quantum Hall isospin ferromagnetic states.[1]
It has been demonstrated that, the GH shift of electron beam in graphene can be observed by the twofold degeneracy of dispersion minimum[10] or by using a beam splitter scanning method.[11]

Summary

Introduction

The fourfold spin-valley degenerate degrees of freedom in bulk graphene can support rich physics and novel applications associated with multicomponent quantum Hall effects[1,2,3] and linear conductance filtering.[4,5,6,7] For the spin-valley quantum Hall effects, it is experimentally demonstrated that, the approximate SU(4) isospin symmetry of Landau levels (LL) in graphene can be broken by interactions such as strong Coulomb interaction, Zeeman effect, and lattice scale interactions, manifesting as quantum Hall isospin ferromagnetic states.[1]. Spin-valley splitting of electron beam in graphene The spin band-gaps and valley wave-vectors in the modulation regions respectively mimic spin- and valley-dependent refractive indices, acting as a spin or valley beam splitter near total reflections.

Results

Conclusion