Quantum anomalous Hall effect in graphene from Rashba and exchange effects

Abstract

We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a non-zero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.

Edge states in graphene-like systems

“…A more realistic model describing another realization of the quantum anomalous Hall state in graphene was proposed by Qiao and coworkers 80,81 . In their model they describe electrons in graphene including both the Rashba spin-orbit term (eq.…”

“…The off-plane exchange field will split the Dirac cones 80,81 , so that the ↑ and ↓ cones are degenerate on a circle in momentum space that, at half filling, corresponds to the Fermi circle. The Rashba term couples ↑ and ↓, opening a band gap in the Fermi circle.…”

“…First, the Haldane model for spinless fermions moving in a honeycomb lattice 21 . Second, graphene perturbed both with a Rashba spin-orbit interaction and subject to an exchange field that couples to the off-plane spin component 80,81 . …”

Magnetic adatoms in two and four terminal graphene nanoribbons: A comparison between their spin polarized transport

“…A hall conductivity, σ H xy of magnitude 2e 2 /h is observed for the case where the Fermi energy lies in the bulk gap. First principle calculations report a bulk gap of almost 5.5 meV in Fe adsorbed GNRs, which should be possible to verify in experiments 36 . Further, in order to avoid any complicacy, such as adatom-adatom interaction, spin-spin correlation etc., we consider very small concentration of magnetic adatoms, so that any interactions other than RSOI and exchange field will not be present.…”

“…For this, we consider a case where TM (particularly Fe) are adsorbed onto ZGNR. The resulting broken structural symmetry gives rise to a Rashba spin-orbit interaction (RSOI) and the hybridization between the carbon π state and the 3d-shell states of magnetic adatoms generates a macroscopic exchange field 36 . A hall conductivity, σ H xy of magnitude 2e 2 /h is observed for the case where the Fermi energy lies in the bulk gap.…”