SU(2)-symmetry in a realistic spin-fermion model for cuprate superconductors

TL;DR

This paper investigates the SU(2) symmetry relating charge order and superconductivity in cuprates, analyzing how dispersion curvature affects this symmetry and its implications for the phase diagram.

Contribution

It provides a detailed analysis of SU(2) symmetry breaking in a realistic spin-fermion model considering full momentum dependence and dispersion curvature effects.

Findings

SU(2) symmetry breaking is generally small with realistic dispersions.

Symmetry is approximately restored in the large paramagnon mass and coupling limit.

The results suggest a scenario explaining the competition between pseudogap and superconductivity.

Abstract

We consider the Pseudo-Gap (PG) state of high-$T_c$ superconductors in form of a composite order parameter fluctuating between 2$p_F$-charge ordering and superconducting (SC) pairing. In the limit of linear dispersion and at the hotspots, both order parameters are related by a SU(2) symmetry and the eight hotspot model of Efetov $\textit{et al.}$ [Nat. Phys. $\bf{9}$, 442 (2013)] is recovered. In the general case however, curvature terms of the dispersion will break this symmetry and the degeneracy between both states is lifted. Taking the full momentum dependence of the order parameter into account, we measure the strength of this SU(2) symmetry breaking over the full Brillouin zone. For realistic dispersion relations including curvature we find generically that the SU(2) symmetry breaking is small and robust to the fermiology and that the symmetric situation is restored in the large paramagnon mass and coupling limit. Comparing the level splitting for different materials we propose a scenario that could account for the competition between the PG and the SC states in the phase diagram of high-$T_c$ superconductors.