Spin-orbit coupled periodic Anderson model: Kondo-Dirac semimetal and orbital-selective antiferromagnetic semimetal

We investigate the periodic Anderson model composed of an itinerant $c$-band and a strongly localized $f$-band, featuring on-site electron-electron interactions in the $f$-orbitals. The two bands interact via a hybridization term with spin-orbit coupling, which enables spin-flip processes. In the non-interacting limit, these profoundly alter the electronic structure, leading to the emergence of flat bands, van Hove singularities, and, most notably, Dirac cones within a single Kondo-Dirac semimetal order. The strongly interacting regime is explored via the determinant quantum Monte Carlo method, in the absence of the sign problem, where we unveil a complete ground-state phase diagram revealing two distinct phases, the Kondo-Dirac semimetal phase and a novel antiferromagnetic semimetal phase. Their characterization by the spectral functions establishes an orbital-selective Mott transition in the antiferromagnetic semimetal phase, marked by the opening of a gap exclusively in the $f$-orbital while Dirac cones persist in the $c$-orbital. Conversely, in the Kondo-Dirac semimetal phase, both $c$- and $f$-orbitals sustain robust Dirac cones. We establish that spin-orbit coupling in the hybridization term gives rise to Dirac cones, which, combined with additional symmetry-breaking conditions, can generate novel topological states.