Control of Competing Superconductivity and Charge Order by Non-equilibrium Currents

We study the competing charge-density-wave and superconducting order in the attractive Hubbard model under a voltage bias, using steady-state non-equilibrium dynamical mean-field theory. We show that the charge-density-wave is suppressed in a current-carrying non-equilibrium steady state. This effect is beyond a simple Joule-heating mechanism and a "supercooled" metallic state is stabilized at a non-equilibrium temperature lower than the equilibrium superconducting $T_c$. On the other hand, a current-carrying superconducting state is always in equilibrium. It is not subject to the same non-thermal suppression, and can therefore nucleate out of the supercooled metal, e.g. in a resistive switching experiment. The fact that an electric current can change the relative stability of different phases compared to thermal equilibrium, even when a system appears locally thermal due to electron-eletron scattering, provides a general perspective to control intertwined orders out of equilibrium.