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To resolve the pairing mechanism in the noncentrosymmetric superconductor NbReSi, this study evaluates its electronic structure and electron-phonon interactions beyond traditional harmonic and adiabatic approximations. The authors find that vibrations of the Nb-Re heavy-metal framework drive over 95% of the coupling, but standard harmonic Migdal-Eliashberg theory overestimates the critical temperature ($T_c$) by more than 60%. By accounting for zero-point anharmonic phonon hardening alongside non-adiabatic vertex corrections from localized Re-$d$ orbitals, the calculations match the experimental $T_c$ (6.5 K) and confirm NbReSi as a conventional, phonon-mediated superconductor.
Standard electron-phonon theory overshoots NbReSi's critical temperature by 60%, showing that zero-point anharmonicity and vertex corrections are strictly required to resolve pairing in heavy transition-metal compounds.
The noncentrosymmetric superconductor NbReSi (Tc=6.5 K) is being actively explored for unconventional pairing that is allowed by its broken inversion symmetry. Despite broad experimental interest, what drives its superconductivity remains an open question. We show that the electronic states at the Fermi level are dominated by Nb and Re $d$-states. Vibrations of the same heavy-metal framework contribute more than 95% of the electron-phonon coupling, with the strongest coupling arising from the sublattice-selective breathing mode involving strongly bonded Re atoms. Harmonic Migdal-Eliashberg theory overestimates Tc by more than 60%. The zero-point anharmonic hardening of these modes reduces the coupling by 20%. The leading vertex correction becomes important as well despite low phonon energies due to the contribution of spatially localized Re-d orbitals to the electronic band structure near the Fermi level. Together, anharmonicity and vertex corrections bring the calculated Tc and superconducting gap into close agreement with experiment, establishing NbReSi as a moderately coupled, phonon-mediated superconductor whose quantitative description requires going beyond harmonic Migdal--Eliashberg theory.