Realization of Odd-Frequencyp-Wave Spin–Singlet Superconductivity Coexisting with Antiferromagnetic Order near Quantum Critical Point

A possibility of the realization of the p-wave spin-singlet superconductivity (pSS), whose gap function is odd both in momentum and in frequency, is investigated by solving the gap equation with the phenomenological interaction mediated by the antiferromagnetic spin fluctuation. The pSS is realized prevailing over the d-wave singlet superconductivity (dSS) in the vicinity of antiferromagnetic quantum critical pint (QCP) both on the paramagnetic and on the antiferromagnetic sides. Off the QCP in the paramagnetic phase, however, the dSS with line-nodes is realized as conventional anisotropic superconductivity. For the present pSS state, there is no gap in the quasiparticle spectrum everywhere on the Fermi surface due to its odd frequency. These features can give a qualitative understanding of the anomalous behaviors of NQR relaxation rate on CeCu₂Si₂ or CeRhIn₅ where the antiferromagnetism and superconductivity coexist on a microscopic level.