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

P. McHale·P. Thalmeier·P. Fulde
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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.

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P. McHale, P. Thalmeier, P. Fulde. 2004-01-26. Strong-coupling theory of magnetic-exciton-mediated superconductivity in UPd$_2$Al$_3$. https://doi.org/10.1103/physrevb.70.014513

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