Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates

TL;DR

This paper investigates the coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates using the spin-fermion model, revealing their interplay with superconductivity and symmetry-breaking effects.

Contribution

It demonstrates that CDW and PDW orders coexist with the same momentum, breaking multiple symmetries, and aligns theoretical predictions with ARPES experimental data.

Findings

Coexistence of CDW and PDW orders with same momentum.

Breaking of $C_4$ symmetry, time-reversal, and mirror symmetries.

Consistency with ARPES data and predictions for experiments.

Abstract

We analyze incommensurate charge-density-wave (CDW) and pair-density-wave (PDW) orders with transferred momenta $(\pm Q,0)$/$(0,\pm Q)$ in underdoped cuprates within the spin-fermion model. Both orders appear due to exchange of spin fluctuations before magnetic order develops.We argue that the ordered state with the lowest energy has non-zero CDW and PDW components with the same momentum. Such a state breaks $C_4$ lattice rotational symmetry, time-reversal symmetry, and mirror symmetries. We argue that the feedback from CDW/PDW order on fermionic dispersion is consistent with ARPES data. We discuss the interplay between the CDW/PDW order and $d_{x^2-y^2}$ superconductivity and make specific predictions for experiments.