Exact theory of superconductivity in a strongly correlated Fermi-arc model

TL;DR

This paper presents an exactly solvable model that captures the coexistence of Fermi arcs and d-wave superconductivity, revealing how Fermi arcs suppress $T_c$ and affect the gap-to-$T_c$ ratio in cuprates.

Contribution

It provides an analytical solution illustrating the impact of Fermi arcs on superconductivity, offering insights into high-$T_c$ superconductor behavior.

Findings

Fermi arcs generate a many-body effect that suppresses $T_c$.

The model reproduces a superconductivity dome as a function of doping.

The gap-to-$T_c$ ratio exceeds the mean-field limit due to Fermi-arc effects.

Abstract

Because the normal state of underdoped cuprate superconductors is an enigmatic Fermi-arc metal, it is valuable to analyze an exactly solvable model that exhibits both Fermi arcs and $d$-wave superconductivity. Here, we focus on a recently proposed solvable model in which the emergence of Fermi arcs is especially transparent. Upon incorporating a $d$-wave pairing interaction, the model produces an asymptotically exact solution for the superconducting transition temperature $T_c$ that traces out a superconductivity dome as a function of hole doping, in qualitative agreement with experimental observations in cuprates. Crucially, we show analytically that the Fermi arcs generate an additional many-body effect that suppresses $T_c$ beyond the simple reduction expected from a shrinking Fermi surface. The many-body nature of the Fermi arcs further introduces the gap-to-$T_c$ ratio greatly surpassing the mean-field limit. These findings provide an analytic benchmark for understanding how Fermi-arc physics competes with $d$-wave superconductivity in high-$T_c$ superconductors.