Vortices and phase transitions in a superconductor with repulsive interactions

We analyze the structure of an s-wave superconducting gap in systems with electron-phonon attraction and electron-electron repulsion. Earlier works have found that superconductivity develops despite strong repulsion, but the gap necessarily changes sign along the Matsubara axis. We analyze the sign-changing gap function from a topological perspective using the knowledge that a nodal point  is the center of dynamical vortex. We consider two models of repulsive interaction and trace the vortex positions along the Matsubara axis and in the upper frequency half plane upon changing the relative strength of the attractive and repulsive

components.  We argue that superconductivity vanishes when a vortex reaches zero frequency and discuss the spectrum of phase fluctuations near this point.