Renormalization-Group Approach to Odd-Frequency Superconductivity

In the BCS theory, Cooper pairs are formed between electrons of opposite momenta near the Fermi surface and condense into the superconducting state. The Eliashberg theory takes into account retardation effects. In these theories, the pairing between electrons occurs at equal times. Here we investigate the off-time pairing, or odd-frequency superconductivity, first introduced by Berezinskii, using a renormalization-group approach. By considering a two-dimensional rotationally invariant Fermi surface at zero temperature, and assuming that the paired electrons have the same spin and opposite momenta near the Fermi surface, we probe the susceptibility of the system to forming Cooper pairs using the method of renormalization-group. We present a self-contained derivation of the flow equations for the vertex function and electron self-energy. We show numerical results for the vertex function in both weak-coupling and strong-coupling cases.