Giant Intrinsic Spin-Orbit Coupling in Bilayer Graphene

TL;DR

This paper reveals that bilayer graphene exhibits a significantly larger intrinsic spin-orbit coupling than monolayer graphene, leading to unique spin polarization states that can be manipulated electrically, with implications for spintronics.

Contribution

The study identifies the dominant hopping processes responsible for ISOC in bilayer graphene and derives the corresponding Hamiltonians, highlighting the enhanced ISOC magnitude and its effects.

Findings

ISOC in bilayer graphene is about 0.46 meV, 100 times larger than in monolayer.

Low-energy states show opposite spin polarization in upper and lower layers.

Spin polarization is robust and can be electrically controlled.

Abstract

The intrinsic spin-orbit coupling (ISOC) in bilayer graphene is investigated. We find that the largest ISOC between $\pi$ electrons origins from the following hopping processes: a $\pi$ electron hops to $\sigma$ orbits of the other layer and further to $\pi$ orbits with the opposite spin through the intra-atomic ISOC. The magnitude of this ISOC is about $0.46meV$, 100 times larger than that of the monolayer graphene. The Hamiltonians including this ISOC in both momentum and real spaces are derived. Due to this ISOC, the low-energy states around the Dirac point exhibit a special spin polarization, in which the electron spins are oppositely polarized in the upper and lower layers. This spin polarization state is robust, protected by the time-reversal symmetry. In addition, we provide a hybrid system to select a certain spin polarization state by an electric manipulation.