Abstract
A many-body system in the vicinity of a first-order phase transition may get trapped in a local minimum of the free energy landscape. These so-called false-vacuum states may survive for exceedingly long times if the barrier for their decay is high enough. The rich phase diagram obtained in graphene multilayer devices presents a unique opportunity to explore transient superconductivity on top of a correlated false vacuum. Specifically, we consider superconductors which are terminated by an apparent first-order phase transition to a correlated phase with different symmetry. We propose that quenching across this transition leads to a non-equilibrium ephemeral superconductor, readily detectable using straightforward transport measurements. Moreover, the transient superconductor also generically enhances the false vacuum lifetime, potentially by orders of magnitude. In several scenarios, the complimentary effect takes place as well: superconductivity is temporarily emboldened in the false vacuum, albeit ultimately decaying. We demonstrate the applicability of these claims for different instances of superconductivity terminated by a first order transition in rhombohedral graphene. The obtained decay timescales position this class of materials as a promising playground to unambiguously realize and measure non-equilibrium superconductivity.