Spiral magnetism and chiral superconductivity in Kondo-Hubbard triangular lattice model

Building on the results of Ref. \cite{faye2018phase}, which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with 120^o spin orientation. In addition to the antiferromagnetic exchange interaction J_perp between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion U of the conduction electrons and the Heisenberg interaction J_H between the impurities. At half-filling, we obtain the quantum phase diagrams in both planes \(J_perp, U J_perp\) and \(J_perp, J_H\). We identify a long-range, three-sublattice, spiral magnetic order which dominates the phase diagrams for small J_perp and moderate U, while a Kondo singlet phase becomes more stable at large J_perp. The transition from the spiral magnetic order to the Kondo singlet phase is a second-order phase transition. In the \(J_perp, J_H\) plane, we observe that the effect of J_H is to reduce the Kondo singlet phase, giving more room to the spiral magnetic order phase. It also introduces some small magnetic oscillations of the spiral magnetic order parameter. At finite doping and when spiral magnetism is ignored, we find superconductivity with symmetry order parameter d+id, which breaks time reversal symmetry. The superconducting order parameter has a dome centered at around 5\% hole doping, and its amplitude decreases with increasing J_perp. We show that spiral magnetism can coexist with d+id state and that superconductivity is suppressed, indicating that these two phases are in competition.