Precursory Cooper Flow in Ultralow-Temperature Superconductors

Superconductivity at low temperature – observed in lithium and bismuth, as well as in various low-density superconductors – calls for developing reliable theoretical and experimental tools for predicting ultralow critical temperatures, $T_c$, of Cooper instability in a system demonstrating nothing but normal Fermi liquid behavior in a broad range of temperatures below the Fermi energy, $T_{\mathrm{F}}$. Equally important are controlled predictions of stability in a given Cooper channel. We identify such a protocol within the paradigm of precursory Cooper flow – a universal ansatz describing logarithmically slow temperature evolution of the linear response of the normal state to the pair-creating perturbation. Applying this framework to the two-dimensional uniform electron gas, we reveal a series of exotic superconducting states, pushing controlled theoretical predictions of $T_c$ to the unprecedentedly low scale of ${10}^{-100}{T}_{\mathrm{F}}$.