Density of states, nuclear relaxation rate, and thermal conductivity in high-Tcsuperconductors

We solve the Eliashberg equations for the self-energy of quasiparticles in a two-dimensional band, interacting via exchange of phonons and antiparamagnons. The interaction due to exchange of spin and charge fluctuations is calculated self-consistently within the random-phase approximation for the Hubbard model. The pair breaking caused by spin fluctuations leads to a gapless density of states near ${\mathit{T}}_{\mathit{c}}$, to a rapid drop of the nuclear-spin-lattice relaxation rate below ${\mathit{T}}_{\mathit{c}}$, and to a gradual upturn of the phonon thermal conductivity below ${\mathit{T}}_{\mathit{c}}$. In the superconducting state there occurs a pseudogap in the dynamical structure factor for neutron scattering. Our results are in qualitative agreement with the experimental data on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$.