We show that the retarded interaction between quasiparticiles on a 2D square lattice induced by the exchange of antiferromagnetic paramagnons leads uniquely to a transition to a superconducting state with ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ symmetry. With a spin-excitation spectrum and a quasiparticle-paramagnon coupling determined by fits to normal-state experiments, we obtain high transition temperatures and energy-gap behaviors comparable to those measured for ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$, ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6.63}$, and ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_4$.

• Received 17 July 1991

DOI:https://doi.org/10.1103/PhysRevLett.67.3448

This article appears in the following collection:

Heating up of Superconductors

This collection marks the 30th anniversary of the discovery of high-temperature superconductors. The papers selected highlight some of the advances that have been made to date, both in understanding why these compounds behave in the way they do, and in utilizing them in applications.