Enhancing superconductivity of A$_{\mathrm{3}}$C$_{\mathrm{60}}$ fullerides : mechanism and its relation to optically stimulated superconductivity

Recently, there was a remarkable observation of the nonequilibrium superconductivity (SC) up to \textasciitilde 100 K in K$_{\mathrm{3}}$C$_{\mathrm{60}}$ fullerides by terahertz (THz) optical pump prove experiment.[Ref.[1]] This temperature (T) of nonequilibrium SC is much higher than T$_{\mathrm{c}}$ of equilibrium (20K). Motivated by the experiment, we investigate how perturbation effects on SC of A$_{\mathrm{3}}$C$_{\mathrm{60}}$ by using the strong-coupling model. We have shown that the perturbation such that smaller Coulomb interaction in two of three LUMO of C$_{\mathrm{60}}$ enhances T$_{\mathrm{c}}$ of fullerides, potentially up to factor of 1.8. We have shown that this type of perturbation could be realized in the pump prove experiment by T$_{\mathrm{1u}}$(4) phonon excitation which is suggested to be pumped from the THz light. Other types of perturbations are detrimental to the SC of fullerides. The mechanism of T$_{\mathrm{c}}$ of fullerides is that (i) stabilization of spin-singlet states, and (ii) preservation orbital fluctuation. This finding provides guideline for experiment to observe an enhancement of T$_{\mathrm{c}}$ and basis for theoretical investigation of nonequilibrium phenomena of fullerides. [1] M. Mitrano et al., Nature 530, 461 (2016).