Konschuh , Sergey and Gmitra, Martin and Kochan, Denis and Fabian, Jaroslav (2012) Theory of spin-orbit coupling in bilayer graphene. Physical Review B (PRB) 85, p. 115423.
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A theory of spin-orbit coupling in bilayer graphene is presented. The electronic band structure of the AB bilayer in the presence of spin-orbit coupling and a transverse electric field is calculated from first principles using the linearized augmented plane-wave method implemented in the wien2k code. The first-principles results around the K points are fitted to a tight-binding model. The main conclusion is that the spin-orbit effects in bilayer graphene derive essentially from the single-layer spin-orbit coupling which comes almost solely from the d orbitals. The intrinsic spin-orbit splitting (anticrossing) around the K points is about 24 μeV for the low-energy valence and conduction bands, which are closest to the Fermi level, similarly as in the single-layer graphene. An applied transverse electric field breaks space inversion symmetry and leads to an extrinsic (also called Bychkov-Rashba) spin-orbit splitting. This splitting is usually linearly proportional to the electric field. The peculiarity of graphene bilayer is that the low-energy bands remain split by 24 μeV independently of the applied external field. The electric field, instead, opens a semiconducting band gap separating these low-energy bands. The remaining two high-energy bands are spin split in proportion to the electric field; the proportionality coefficient is given by the second intrinsic spin-orbit coupling, whose value is 20 μeV. All the band-structure effects and their spin splittings can be explained by our tight-binding model, in which the spin-orbit Hamiltonian is derived from symmetry considerations. The magnitudes of intra- and interlayer couplings—their values are similar to the single-layer graphene ones—are determined by fitting to first-principles results.
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Richter > Group Jaroslav Fabian|
|Projects:||SFB 689: Spinphänomene in reduzierten Dimensionen, GRK 1570, Elektronische Eigenschaften von Nanostrukturen auf Kohlenstoff-Basis|
|Keywords:||graphene, spin-orbit coupling|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Owner:||Prof. Dr. Jaroslav Fabian|
|Deposited On:||08 May 2012 12:38|
|Last Modified:||08 May 2012 12:38|