Quantum phase transition in a clean superconductor with repulsive dynamical interaction

Abstract

We consider a model of electrons at zero temperature, with a repulsive interaction which is a function of the energy transfer. Such an interaction can arise from the combination of electron-electron repulsion at high energies and the weaker electron-phonon attraction at low energies. As shown in previous works, superconductivity can develop despite the overall repulsion due to the energy dependence of the interaction, but the gap $\Delta (\omega )$ must change sign at some (imaginary) frequency ${\omega }_0$ to counteract the repulsion. However, when the constant repulsive part of the interaction is increased, a quantum phase transition towards the normal state occurs. We show that, as the phase transition is approached, $\Delta$ and ${\omega }_0$ must vanish in a correlated way such that $1/|\log [\Delta (0)]|\sim {\omega }_0^2$. We discuss the behavior of phase fluctuations near this transition and show that the correlation between $\Delta (0)$ and ${\omega }_0$ locks the phase stiffness to a non-zero value.

journal version

References in corpus (2)

• Pairing from dynamically screened Coulomb repulsion in bismuth
• The Effect of Repulsion on Superconductivity at Low Density

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• Odd frequency pairing in a quantum critical metal
• Odd-frequency pairing and time-reversal symmetry breaking for repulsive interactions