Energy scale of the electron-boson spectral function and superconductivity inNpPd5Al2

Abstract

The energy scale ${\ensuremath{\Omega}}_{0}$ of the electron-boson spectral function in the heavy-fermion, $d$-wave superconductor ${\text{NpPd}}_{5}{\text{Al}}_{2}$ is predicted on the basis of Eliashberg theory calculations. Assuming a spectral function shape typical for antiferromagnetic spin fluctuations, and imposing constraints provided by the experimental values for the critical temperature and the low-temperature energy gap, one obtains values of ${\ensuremath{\Omega}}_{0}$ of about 2--2.5 meV, slightly dependent from the strength of the Coulomb pseudopotential. These values are in excellent agreement with the characteristic magnetic fluctuations energy estimated from NMR measurements of the nuclear-spin-lattice relaxation time at the Al site. The calculated temperature dependence of the upper critical field, the local spin susceptibility, and the nuclear-spin-lattice relaxation rate is also in good agreement with available experimental data, showing that a coherent description of the superconducting state can be obtained assuming that the electron pairing in ${\text{NpPd}}_{5}{\text{Al}}_{2}$ is mediated by antiferromagnetic fluctuations. We finally report predictions for the London penetration depth, the energy dependence of the tunneling differential conductance at different temperatures, and the temperature dependence of the energy gap.