RG analysis and Magnetic instability in gapless superconductors

TL;DR

This paper investigates magnetic instabilities in gapless superconductors, revealing how Fermi-surface mismatch influences the emergence of secondary gaps or supercurrent condensates, and analyzing their magnetic properties.

Contribution

It provides a detailed analysis of magnetic instabilities and phase transitions in gapless superconductors, including the formation of supercurrent condensates and their magnetic characteristics.

Findings

Quadratic dispersion of gapless modes near the Fermi surface

Transition to a supercurrent condensate phase at large mismatch

Positive Meissner mass orthogonal to condensate direction

Abstract

We study the magnetic instability of gapless superconductors. The instability arises due to the infrared divergence associated with the gapless modes of the superconductor. When the Fermi-surface mismatch between pairing fermions is close to the gap, the gapless modes have a quadratic energy dispersion relation at low energy and open a secondary gap at the Fermi surface, which is only power-suppressed by the coupling. On the other hand, for a large mismatch, we find the gapless superconductor does not open a secondary gap, but instead makes transition to a new phase by forming the condensate of supercurrents. We calculate the condensate of supercurrents by minimizing the effective potential. In the new phase, the Meissner mass is positive for the magnetic fields orthogonal to the direction of the condensate but zero in the parallel direction.