Kitaev interactions in metallic bands and resulting Berry curvature distributions

The Kitaev spin model on a honeycomb lattice with competing bond-dependent interactions describes a quantum spin liquid (QSL) with topological order and fractionalized excitations. Such models can be realized in Mott insulators withstrong spin-orbit coupling. The main question we ask is: what is the manifestation of the bond-dependent frustration in the opposite weakly correlated metallic limit? We investigate a symmetry-allowed tight binding model on a honeycomb lattice with 5d t_2g orbitals (L_eff=−1) in the presence of strong atomic spin-orbit coupling. We choose the parameters of this tightbinding model such that in the strong coupling limit it reproduces the Heisenberg and Kitaev spin Hamiltonians. We find that the band touching points move from K/K′, for the tightbinding parameters corresponding to the Heisenberg Hamiltonian, to M and Γ for the Kitaev parameters. Furthermore, for the Kitaev parameters, the frustration is reflected in extremely flat bands. We calculate the effect of the evolution of the Berry curvature on the linear and nonlinear electromagnetic response.