Superconductivity and spin-density waves: Application to heavy-fermion materials

We examine possible superconducting (SC) pairing states competing with the spin-density wave (SDW). On the basis of an imperfect-nesting-band model in two dimensions, we investigate a Hamiltonian including the on-site repulsive interaction in addition to the attractive interaction within a mean-field approximation. The present theory is applicable in a unified way to both $T_c$>$T_N$ and $T_c$<$T_N$, where $T_c$($T_N$)is the transition temperature of the SC (SDW). It is shown that anisotropic pairing states enumerated group theoretically can be categorized into two classes: less-competitive and competitive states according to the combined symmetry of the SC order parameter (parity and translational symmetry determined by the nesting vector). In the presence of the SDW the less-competitive states that include both odd- and even-parity states are stabilized, but definitely exclude the isotropic singlet state. We discuss the experimental implication of our theory to the heavy-fermion superconductors ${\mathrm{URu}}_2$${\mathrm{Si}}_2$, (U,Th)${\mathrm{Be}}_{13}$, (U,Th)${\mathrm{Pt}}_3$, and U(Pt,Pd${)}_3$, which all exhibit the Fermi-surface-related SDW instability.