Precursory Cooper flow in ultralow-temperature superconductors

Abstract

Superconductivity at low temperature—observed in lithium and bismuth, as well as in various low-density superconductors—calls for the development of reliable theoretical and experimental tools for predicting ultralow critical temperatures T_{c} of Cooper instability in a system demonstrating simply normal Fermi liquid behavior in a broad range of temperatures below the Fermi energy T_{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_{F}.