Renormalization group analysis of the pair-density-wave and charge order within the fermionic hot-spot model for cuprate superconductors

TL;DR

This study uses a two-loop renormalization group analysis of the fermionic hot-spot model to explore charge-density-wave and pair-density-wave orders in cuprate superconductors, revealing conditions under which these orders become dominant.

Contribution

It extends previous hot-spot model analyses by including two-loop RG calculations and investigates the competition between CDW and PDW orders, highlighting their potential dominance at moderate coupling strengths.

Findings

CDW and PDW are nearly degenerate and linked by an emergent SU(2) symmetry.

Both orders are subleading compared to antiferromagnetism, BDW, and SSC at weak couplings.

Increasing coupling strength favors PDW/CDW as leading orders, suggesting relevance for high-temperature cuprate phases.

Abstract

In light of the new experimental and theoretical important developments in high-$T_c$ superconductivity, we revisit the fermionic hot-spot model relevant to the phenomenology of the cuprates. We extend previous results by means of a complete two-loop order renormalization group (RG) framework. Here, we explicitly study the effect of the charge-density-wave (CDW) order parameter with a $d$-wave form factor with the experimentally observed modulation $(\pm Q_0,0)$ and $(0,\pm Q_0)$ at the infrared-stable nontrivial fixed point obtained previously for this model. Additionally, we proceed to investigate also the so-called pair-density-wave (PDW) order that was recently proposed in the literature as a possible candidate for the "hidden" order to describe the pseudogap phase observed in underdoped cuprates. We confirm that although the above two ordering tendencies are also found to be nearly degenerate both at one-loop and two-loop RG orders and linked by an emergent $SU(2)$ pseudospin symmetry, they turn out to be subleading for weaker couplings in the present model to antiferromagnetism, $d$-wave bond-density wave (BDW) order with modulation along Brillouin zone diagonals $(\pm Q_0,\pm Q_0)$, and $d$-wave singlet superconductivity (SSC). However, as we increase the strength of the initial coupling towards moderate values, we do capture a tendency for the entangled PDW/CDW order to become leading compared to BDW/SSC in the model, which suggests that the former composite order might be indeed a viable concept to describe some cuprate superconductors at high temperatures in the underdoped regime, as has been recently alluded to by many authors in the literature.