Variational cluster approach to superconductivity and magnetism in the Kondo lattice model

We investigate in detail antiferromagnetic (AF) and superconducting (SC) phases as well as their coexistence in the two-dimensional Kondo lattice model on a square lattice, which is a paradigmatic model for heavy fermion materials. The results presented are mainly obtained using the variational cluster approximation (VCA) and are complemented by analytical findings for the equations of motion of pairing susceptibilities. A particularly interesting aspect is the possibility to have s-wave SC near half filling as reported by Bodensiek \textit{et al.} [Phys. Rev. Lett. \textbf{110}, 146406 (2013)]. When doping the system, we identify three regions which correspond to an AF metallic phase with small Fermi surface at weak coupling, an AF metal with a different Fermi surface topology at intermediate coupling, and a paramagnetic metal with a large Fermi surface at strong coupling. The transition between these two AF phases is found to be discontinuous at lower fillings, but turns to a continuous one when approaching half-filling. In the quest for s-wave superconductivity, only solutions are found which possess mean-field character. No true superconducting solutions caused by correlation effects are found in the s-wave channel. In contrast, we clearly identify robust d-wave pairing away from half-filling. However, we show that only by treating antiferromagnetism and superconductivity on equal footing artificial superconducting solutions at half-filling can be avoided. Our VCA findings support scenarios previously identified by variational Monte Carlo approaches and are a starting point for future investigations with VCA and further approaches such as cluster-embedding methods.