Theoretical Study on the Interplay of Spin-Density Wave and Superconductivity: Critical Temperature and the Gap-to-Tc Ratio

Abstract

At low temperatures, strong electronic correlations in many unconventional superconductors can induce a spin-density-wave (SDW) state as a result of Fermi-surface nesting and enhanced electron–electron interactions, and such SDW order is frequently observed to compete or coexist with superconductivity in correlated materials. In this work, we investigate the coexistence of SDW order and superconductivity using the Green’s function method in the Nambu representation, incorporating both electron–phonon-mediated pairing and pairing associated with SDW order at the antiferromagnetic wave vector. Two cases of gap equations are found to yield identical expressions for the superconducting critical temperature and the zero-temperature order parameter. Our results show that as the SDW order parameter increases, a larger coupling constant is required for superconductivity to emerge. Moreover, the gap-to-Tc ratio exceeds the BCS value at intermediate SDW strength and subsequently decreases to values below the BCS limit as the ratio of the zero-temperature SDW order parameter to the superconducting gap increases.