Suppression of electron-phonon mediated superconductivity by strong spin fluctuation effects in the 2D Ising superconductor NbSe₂

Two-dimensional materials particularly transition metal dichalcogenides (TMDs) are promising candidates for atomically thin electronic applications, such as spintronic, valleytronic, and quantum hall devices. A later addition to the landscape pertains to the discovery of an unusual superconducting state in monolayers of NbSe₂ dubbed ‘Ising superconductivity’. It is generally believed that the superconductivity of monolayer NbSe₂ is dominated primarily by electron-phonon effects. However, comparison with the experiment indicates that conventional first-principles calculation of the electron-phonon coupling severely overestimates the critical temperature and superconducting gap. Since it was recently found that this system is close to a magnetic instability, and given that the first principles Eliashberg theory has been very successful in the prediction of the superconducting temperature in phonon superconductors, it is natural to assume that superconductivity in NbSe2 is partially suppressed by spin fluctuations. In our work, we include the latter on the level of Berk-Schrieffer's theory. It appears crucially important to include retardation effects accounting for the different energy scales of phonons and paramagnons. Both momentum and frequency dependence of spin-fluctuations were extracted from ab initio calculations, along with the full electron-phonon momentum-resolved Eliashberg function. After solving the full band and momentum-resolved Eliashberg equations, we extracted the momentum and temperature-dependent order parameter, as well as the critical temperature. We then investigated the average order parameter averaged over each Fermi surface, as well as over the all electronic state, and after comparison with the tunneling data, discuss, as to what level the calculated anisotropy survives in real samples.