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

TL;DR

This paper investigates the coexistence of charge order, pseudogap phenomena, and pairing density waves in cuprate superconductors, highlighting the role of SU(2) symmetry and Fermi surface shape in these emergent states.

Contribution

It introduces a new analysis of the spin-fermion model at hot spots, revealing stable solutions that include coexisting charge density waves and pairing fluctuations under SU(2) symmetry.

Findings

Charge density wave coexists with pairing fluctuations at low temperature.

Charge density wave sensitivity depends on Fermi surface shape.

SU(2) symmetry links charge order and pairing density wave states.

Abstract

We address the timely issue of the presence of charge ordering at the hot-spots in the pseudo-gap 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 the hot spots. A careful examination of their stability and free energy shows that, at low temperature, the system tends towards a co-existence of charge density wave (CDW) and the composite order parameter made of diagonal quadrupolar density wave and pairing fluctuations of Ref. [Nat. Phys. $\bf{9}$, 1745 (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 pseudo-gap phase also applies to the CDW state, which therefore admits a pairing density pave counterpart breaking time reversal symmetry.