Odd-frequency pair density wave correlations in underdoped cuprates

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 modulation or wave is also ubiquitously found underdoped cuprates. Within a general mean-field one-band model we show that the coexistence of waves and uniform superconductivity $d$-wave like cuprates, generates an odd-frequency spin-singlet pair wave, addition to even-frequency counterparts. The strength induced depends on vector even becoming comparable ones parts Brillouin zone. We change from bi-axial uni-axial, can enhance component waves. Such uni-axial has already experimentally verified at magnetic fields further discuss possibility spin-triplet generated regime spin applicable iron-based superconductors. Our work thus presents route bulk T$_c$