The effects of spin-orbit coupling on the Anderson lattice model: correlated Kondo-Dirac semimetal and orbital selective antiferromagnetic semimetal phases.

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 (DQMC) 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 reveals an orbital-elective 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.