Theory of the nonlinear susceptibility of layered superconductors: application to strontium ruthenate*

Probing superconducting fluctuations (SF) in unconventional superconductors is essential to elucidate their nature. Much work has been done to elucidate the contributions from SF to the conductivity and the linear susceptibility, disentangling them from normal state contributions can be challenging. An alternative that has been recently explored is to measure the nonlinear susceptibility via third-order magnetic response, which is believed to be dominated by SF above T_c. Here, we present a phenomenological theoretical model for the nonlinear susceptibility of layered superconductors. Our model, based on the Lawrence-Doniach functional, predicts power-law behaviors in distinct temperature and magnetic field regimes. Comparison with data from conventional BCS superconductors reveals an excellent agreement between theory and experiment. The same does not happen, however, for oxide superconductors, such as the strontium ruthenate Sr₂RuO₄ [D Pelc et al., Nat. Commun. 10, 2729 (2019)]. We show that inclusion of disorder can capture some of the experimental features. Finally, we discuss the limitations and possible extensions of our model.