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We investigate the competition between superconductivity, charge-ordering,magnetic-ordering, and the Kondo effect in a heavy fermion $s$-wavesuperconductor described by a Kondo lattice model with an attractive on-siteHubbard interaction. The model is solved using the real-space dynamical meanfield theory. For this purpose, we develop a numerical renormalization group(NRG) framework in Nambu space, which is used to solve the superconductingimpurity problem. This extended NRG scheme also allows for SU(2) spin symmetrybroken solutions, enabling us to examine the competition or cooperation between$s$-wave superconductivity and incommensurate spin-density waves (SDWs). Athalf filling, we find an intriguing phase where the magnetic ordering of the$f$-electrons lifts the degeneracy between the charge density wave (CDW) stateand the superconducting state, leading to a strong suppression ofsuperconductivity. In addition, the system may also become a half metal in thisparameter regime. Away from half filling, the CDWs vanish and are replaced bysuperconductivity combined with incommensurate SDWs up to moderate Kondocouplings to the $f$-electrons. We find that both CDWs as well assuperconductivity enhance magnetic ordering due to the suppression of Kondoscreening.

Interplay between charge, magnetic and superconducting order in a Kondo lattice with an attractive Hubbard interaction