Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving

The resonant excitation of mid-infrared phonon modes provides a new way of controlling material properties. An interesting result of such experiments is a light-induced superconducting (SC)-like behavior [1], for which several possible mechanisms have been theoretically proposed. However, in driven systems, the competition from heating and nonthermal energy distributions must be taken into account in order to assess the ultimate effect of such nonequilibrium states on SC.

In the present work, we focus on the scenario that the parametric excitation of Raman-active phonons through nonlinear couplings to the mid-infrared phonons enhances the phonon-mediated attractive interaction and hence SC [2]. We systematically investigate the effects of the parametric phonon driving on SC in the Holstein model by analyzing the transient dynamics and the non-equilibrium steady states (NESS) using the non-equilibrium dynamical mean-field theory [3]. For NESS, the Floquet dynamical mean-field theory for electron-phonon systems is newly formulated. In the strong electron-phonon coupling regime, even though the attractive interaction can indeed be enhanced by the driving, the SC gap and the superfluid density are always suppressed in the NESS, in particular, at the parametric resonance. Even in the transient dynamics towards the NESS, the net effect is a suppression of SC. In the weakly-coupled regime, we study how the SC fluctuations evolve under the driving. Generically these correlations decay faster in the presence of driving and the decay becomes particularly fast around the parametric resonance. Our systematic analysis shows that, in a wide parameter range, the heating of the system is the dominant effect and that the parametric phonon driving has a negative effect on SC.

[1] M. Mitrano, et al., Nature 530, 461 (2016).
[2] M. Knap, et al., Phys. Rev. B 94, 214504 (2016); M. Babadi, et al., Phys. Rev. B 96, 014512 (2017).
[3] Y. Murakami, et al., Phys. Rev. B 96, 045125 (2017).