Pseudogap, charge order, and pairing density wave at the hot spots in cuprate superconductors

We address the timely issue of the presence of charge ordering at the hot spots in the pseudogap phase of cuprate superconductors in the context of an emergent SU(2) symmetry which relates the charge and pairing sectors. Performing the Hubbard-Stratonovich decoupling such that the free energy stays always real and physically meaningful, we exhibit three solutions of the spin-fermion model at hot spots. A careful examination of their stability and free energy shows that, at low temperatures, the system tends towards the coexistence of a charge density wave (CDW) and the composite order parameter made up of the diagonal quadrupolar density wave and pairing fluctuations of K. B. Efetov et al. [Nat. Phys. 9, 442 (2013)]. The CDW is sensitive to the shape of the Fermi surface, in contrast to the diagonal quadrupolar order, which is immune to it. SU(2) symmetry within the pseudogap phase also applies to the CDW state, which therefore admits a pairing density p-wave counterpart breaking time-reversal symmetry.