Spin-orbit coupling and broken spin degeneracy in multilayer graphene

Edward McCann, Mikito Koshino

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

Since the lattices of ABA -stacked graphene multilayers with an even number of layers, as well as that of monolayer graphene, satisfy spatial-inversion symmetry, their electronic bands must be spin degenerate in the presence of time-inversion symmetry. In intrinsic monolayer and bilayer graphene, when symmetry is not broken by external fields, the only spin-orbit coupling present at low energy near the corner of the Brillouin zone is the Kane-Mele term, that opens a bulk energy gap but does not break the spin degeneracy of the energy bands. However, spin splitting is allowed in multilayers with an odd number of layers (≥3) because their lattices do not satisfy spatial-inversion symmetry. We show that, in trilayer graphene, in addition to the Kane-Mele term, there is a second type of intrinsic spin-orbit coupling present at low energy near the corner of the Brillouin zone. It introduces a Zeeman-type spin splitting of the energy bands at each valley with an opposite sign of the effective magnetic field in the two valleys. We estimate the magnitude of the effective field to be ∼2T.

Original languageEnglish
Article number241409
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume81
Issue number24
DOIs
Publication statusPublished - 2010 Jun 15

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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