Pairing via Index theorem

TL;DR

This paper proposes a mechanism for pairing in doped $ ext{pi}$-flux phases of cuprates, where pairing symmetry depends on quantum tunneling of gauge flux quanta, revealing a zero-temperature critical point.

Contribution

It introduces a novel mechanism linking pairing symmetry to gauge flux tunneling in the doped $ ext{pi}$-flux phase of the t-J model.

Findings

Pairing symmetry varies with tunneling parameter.

A critical point separates different pairing symmetries.

The mechanism explains the evolution of pairing in cuprates.

Abstract

This work is motivated by a specific point of view: at short distances and high energies the undoped and underdoped cuprates resemble the $\pi$-flux phase of the t-J model. The purpose of this paper is to present a mechanism by which pairing grows out of the doped $\pi$-flux phase. According to this mechanism pairing symmetry is determined by a parameter controlling the quantum tunneling of gauge flux quanta. For zero tunneling the symmetry is $d_{x^2-y^2}+id_{xy}$, while for large tunneling it is $d_{x^2-y^2}$. A zero-temperature critical point separates these two limits.