Tight-binding theory of the spin-orbit coupling in graphene

Abstract

The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the ⌫ point is similar to the splitting of the p orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the K point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of 1 eV, based on the -coupling. All-electron first-principles calculations give much higher values, between 25 and 50 eV, due to the presence of the orbitals of the d symmetry in the Bloch states at K. A realistic multiband tight-binding model is presented to explain the effects the d orbitals play in the spin-orbit coupling at K. The -coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling ͑of the Bychkov-Rashba type͒, appearing in the presence of a transverse electric field, is dominated by the -hybridization, in agreement with previous theories. Tightbinding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.

Spin-dependent Klein tunneling in graphene: Role of Rashba spin-orbit coupling

“…Spin-orbit interactions can be incorporated into the TBM by altering the spin-dependent hopping between nearest and next-nearest neighbors, 7,35 modifying Eq. (3) as…”

Electron-electron interactions and topology in the electronic properties of gated graphene nanoribbon rings in Möbius and cylindrical configurations

“…[37][38][39] Graphene nanoribbons also played an important role in inspiring the field of topological insulators. [6][7][8][9][10][11][12] The interior of the graphene ribbon acts like an insulator with a gap in the energy spectrum, whereas the energies of the edge states are in the middle of the gap. The topological aspect of the edge states is generated by the spin-orbit coupling which lifts the spin degeneracy at a given edge, leading to graphene nanoribbon as a spin Hall insulator.…”

“…6 Unfortunately, spin-orbit coupling in graphene is found to be too small to give rise to a spin Hall effect. 10 Interestingly, it has been suggested that nontrivial properties of graphene nanoribbons can be generated directly by engineering a nontrivial Möbius geometry of the nanoribbon without the need for the spin-orbit coupling. [40][41][42][43][44][45][46][47][48][49][50][51] For example, it was shown by Guo et al 46 that one electron states of a class of Möbius graphene ribbons with zigzag edges can be understood by introducing a non-Abelian gauge field 46 as in topological insulators.…”

Electronic spin transport in dual-gated bilayer graphene

“…Graphene is considered to be a promising spin-channel material for future spintronics applications 1 because of its high-electronic mobility, 2 weak spin-orbit coupling 3,4 and a negligible hyperfine interaction. 5,6 The initial spin transport studies were mainly performed on single-layer [7][8][9][10] and bilayer exfoliated graphene, 9,11 and large-area graphene [12][13][14][15] deposited on conventional SiO 2 substrates.…”