Odd-frequency pair density wave correlations in underdoped cuprates

TL;DR

This paper demonstrates that in underdoped cuprates, the coexistence of charge density waves and superconductivity can induce odd-frequency pair density waves, revealing a new form of superconducting correlations with potential implications for high-temperature superconductivity.

Contribution

The study shows that charge density wave and superconductivity coexistence in cuprates generates odd-frequency pair density waves, a novel insight into unconventional superconducting states.

Findings

Odd-frequency pair density waves can be comparable to even-frequency ones.

Changing charge density wave modulation enhances odd-frequency components.

Coexistence of superconductivity and charge density wave observed experimentally.

Abstract

Pair density waves, identified by Cooper pairs with finite center-of-mass momentum, have recently been observed in copper oxide based high T$_\textrm{c}$ superconductors (cuprates). A charge density modulation or wave is also ubiquitously found in underdoped cuprates. Within a general mean-field one-band model we show that the coexistence of charge density waves and uniform superconductivity in $d$-wave superconductors like cuprates, generates an odd-frequency spin-singlet pair density wave, in addition to the even-frequency counterparts. The strength of the induced odd-frequency pair density wave depends on the modulation wave vector of the charge density wave, with the odd-frequency pair density waves even becoming comparable to the even-frequency ones in parts of the Brillouin zone. We show that a change in the modulation wave vector of the charge density wave from bi-axial to uni-axial, can enhance the odd-frequency component of the pair density waves. Such a coexistence of superconductivity and uni-axial charge density wave has already been experimentally verified at high magnetic fields in underdoped cuprates. We further discuss the possibility of an odd-frequency spin-triplet pair density wave generated in the coexistence regime of superconductivity and spin density waves, applicable to the iron-based superconductors. Our work thus presents a route to bulk odd-frequency superconductivity in high T$_c$ superconductors.