A phase diagram for light-induced superconductivity in $kappa$-(ET)$_2$-X

Resonant optical excitation of certain molecular vibrations in $kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br has been shown to induce transient superconducting-like optical properties at temperatures far above equilibrium $T_c$. Here, we report experiments across the bandwidth-tuned phase diagram of this class of materials, and study the Mott insulator $kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Cl and the metallic compound $kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We find non-equilibrium photoinduced superconductivity only in $kappa$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, indicating that the proximity to the Mott insulating phase and possibly the presence of preexisting superconducting fluctuations are pre-requisites for this effect.