Linear Response Approach to Superconducting Phase Transition Temperature

Superconductivity from repulsive interaction has been extensively studied theoretically and experimentally, but determining critical temperature T_c remains challenging due to the exponential smallness of T_c. We propose a novel approach to detect and quantify Cooper instability by monitoring the divergence of the linear response to a symmetry breaking perturbation, and demonstrate that this approach allows an accurate prediction of T_c from known system properties at T»T_c. We establish the phase diagram of the three dimensional(3D) and two dimensional(2D) uniform electron gas(UEG) in the dense limit where the random phase approximation(RPA) is controlled, including quantum critical points for various symmetry channels as the value of r_s is decreased.