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

We consider the pseudogap (PG) state of high-T-c superconductors in the form of a composite order parameter fluctuating between 2p(F)-charge ordering and superconducting (SC) pairing. In the limit of linear dispersion and at the hot spots, both order parameters are related by a SU(2) symmetry, and the eight-hot-spot model of Efetov et al. [Nat. Phys. 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 SC states in the phase diagram of high-T-c superconductors.