New gap equation for a marginal Fermi liquid

TL;DR

This paper derives a new gap equation for a marginal Fermi liquid that emphasizes kinetic energy gain in superconductivity, particularly relevant for high-$T_c$ cuprates with d-wave pairing.

Contribution

It introduces a novel gap equation incorporating kinetic energy effects, applicable to systems with a phenomenological self-energy and repulsive pairing interactions.

Findings

Kinetic energy gain can dominate in high-$T_c$ superconductors.

The new gap equation favors s-wave pairing with repulsive interactions.

Implications for d-wave pairing in cuprates are discussed.

Abstract

Assuming a phenomenological self-energy $Im \Sigma(\omega) \sim |\omega|^{\beta\}, (\beta=1 $), which becomes gapped below $T_c$, we derived a new gap equation. The new gap equation contains the effect of the kinetic energy gain upon developing a superconducting order parameter. However, this new kinetic energy gain mechanism works only for a repulsive pairing potential leading to a s-wave state. In this case, compared to the usual potential energy gain in the superconducting state as in the BCS gap equation, the kinetic energy gain is more effective to easily achieve a high critical temperature $T_c$, since it is naturally Fermi energy scale. In view of the experimental evidences of the d-wave pairing state in the hole-doped copper-oxide high-$T_c$ superconductors, we discuss the implications of our results.