Magnetism and superconductivity in underscreened Kondo chains

We present a one dimensional model of electrons coupled to localized moments of spin $S\ge 1$ in which magnetism and superconductivity interplay in a nontrivial manner. This model has a non-Fermi liquid ground state of the chiral spin liquid type. A non-conventional odd-frequency pairing is shown to be the dominant instability of the system, together with antiferromagnetism of the local moments. We argue that this model captures the physics of the Kondo-Heisenberg spin S=1 chain, in the limit of strong Kondo coupling. Finally, we discuss briefly the effect of interchain coupling.