Quantum Anomalous Hall Effect in Graphene Proximity Coupled to an Antiferromagnetic Insulator

We propose realizing the quantum anomalous Hall effect by proximity coupling graphene to an antiferromagnetic insulator that provides both broken time-reversal symmetry and spin-orbit coupling. We illustrate our idea by performing ab initio calculations for graphene adsorbed on the (111) surface of ${\mathrm{BiFeO}}_3$. In this case, we find that the proximity-induced exchange field in graphene is about 70 meV, and that a topologically nontrivial band gap is opened by Rashba spin-orbit coupling. The size of the gap depends on the separation between the graphene and the thin film substrate, which can be tuned experimentally by applying external pressure.

Figure 1

(a) Supercell for graphene on a (111) ${\mathrm{BiFeO}}_3$ surface. Gray (the top layer), purple (large), yellow (medium), and red (small) colors represent, respectively, C, Bi, Fe, and O atoms. (b) A top view of graphene with one layer of iron atoms. One Fe atom is located at the hollow site labeled by $H$, while the other two Fe atoms are located at the top sites labeled as $A$ and $B$. (c) Band structure along high symmetry lines for a $4\times 4$ supercell of graphene.

Figure 2

Bulk band structure of graphene on ${\mathrm{BiFeO}}_3$. (a) Spin-resolved band structures. (b) Zoom in on the green box of panel (a). The blue (thin) and red (thick) in panels (a) and (b) plot the spin-up and spin-down bands, respectively. (c) Band structure when spin-orbit coupling is included. A bulk gap $\delta$ of about 1.1 meV is centered on the avoided crossings near the $K$ and $K^{\prime }$ valleys. Note that the nontrivial band gap $\delta$ is inside the bulk gap $\mathrm{\Delta }$ of ${\mathrm{BiFeO}}_3$. (d) Zoom in on the green box of panel (c).

Figure 3

Berry curvature along high symmetry lines summed over occupied valence bands below.

Figure 4

(a) Bulk band gap $\delta$ as a function of a change ($d_0-d$) in the separation between the graphene sheet and the ${\mathrm{BiFeO}}_3$ ($d_0$ is the optimal distance obtained from the full relaxation). The square and circle symbols refer, respectively, to gaps from density ab initio calculations and gaps from the low-energy model with the staggered sublattice potential set to zero. (b) Exchange field $M$ as a function of ($d_0-d$). (c) Rashba spin-orbit coupling strength as a function of ($d_0-d$).

Figure 5

Anomalous Hall conductance as a function of Fermi level calculated from the tight-binding model Hamiltonian corresponding to Eq. (1).