Strong-coupling theory of magnetic-exciton-mediated superconductivity in UPd$_2$Al$_3$

TL;DR

This paper develops a strong-coupling theory for superconductivity in UPd$_2$Al$_3$, showing how magnetic excitons mediate pairing, leading to specific gap symmetries and properties consistent with experimental observations.

Contribution

It introduces a dual model with maximal spin anisotropy to compute $T_c$, mass renormalisation, and pairing states, advancing understanding of magnetic-exciton-mediated superconductivity.

Findings

Identifies two opposite-spin pairing states with line nodes perpendicular to c-axis.

Predicts total spin component $S_z$=0, consistent with Knight shift and $H_{c2}$ data.

Shows $T_c$ dependence on a phenomenological coupling constant $g$.

Abstract

There is compelling evidence from inelastic-neutron-scattering and tunneling experiments that the heavy-fermion superconductor UPd$_2$Al$_3$ can be understood as a dual system consisting of magnetic excitons, arising from crystal-field-split U$^{4+}$ levels, coupled to delocalised f-electrons. We have computed the superconducting transition temperature and the mass renormalisation arising from a dual model with maximal spin anisotropy using a strong-coupling approach. We find an instability to two possible opposite-spin-pairing states with even- or odd-parity gap functions. Each has a line node perpendicular to the c-direction, in agreement with NMR relaxation-rate, specific-heat and thermal-conductivity measurements. In addition, both have total spin component $S_z$=0, compatible with the observation of a pronounced Knight shift and $H_{c2}$ Pauli limiting. For parameter values appropriate to UPd$_2$Al$_3$, we determine the dependence of the superconducting transition temperature $T_c$ on a phenomenological coupling constant $g$ and we investigate the associated mass enhancement and its anisotropy.