Theoretical Study of the Interplay between Superconductivity and Antiferromagnetism in f-electron UPd2Al3 Superconductor

: This work presents a theoretical investigation of the effective interplay between superconductivity and antiferromagnetism in the f-electron heavy-fermion superconductor UPd 2 Al 3 . An extended two-band mean-field Hamiltonian, incorporating electron-pairing interactions, localized 5f-electron exchange interactions, and hybridization between itinerant conduction electrons and localized 5f electrons, is formulated. Using the double-time temperature-dependent retarded Green's function formalism, self-consistent equations for the superconducting energy gap (Δ) and the magnetic order parameter (η) are derived. The numerical calculations and the resulting phase diagrams reveal the dependence of the superconducting transition temperature (T C ), magnetic ordering temperature (T m ), and the corresponding order parameters on the relevant interaction strengths. In particular, T C exhibits a nonlinear increase with the effective pairing interaction parameter (λ), whereas the superconducting energy gap decreases continuously with increasing temperature and vanishes at the superconducting transition temperature. The analysis further demonstrates that antiferromagnetic ordering significantly influences the superconducting state through its coupling to η, while T m is strongly enhanced by the magnetic exchange interaction and hybridization effects. The calculated phase diagrams indicate that superconductivity and antiferromagnetism coexist over a broad parameter range and are strongly coupled through the interaction between itinerant conduction electrons and localized uranium 5f electrons. These findings demonstrate that the proposed effective theoretical model captures the coupled coexistence and competition between superconductivity and antiferromagnetism in UPd 2 Al 3 . Furthermore, the present study provides a useful theoretical framework for understanding unconventional heavy-fermion superconductivity and may serve as a basis for future theoretical and experimental investigations of strongly correlated f -electron systems.