Is there a bulk pair density wave in any cuprate
In plain words
A pair density wave is a superconductor whose pair amplitude oscillates in space like a standing wave; hints of it appear in tunneling maps, around magnetic vortices and in one stripe-ordered cuprate.
Precise statement
Determine whether a pair-density-wave order parameter $\Delta_Q$ with period 4 to 8 lattice constants exists as a bulk phase with long-range or quasi-long-range order at zero magnetic field in any cuprate, for example La2-xBaxCuO4 at $x = 1/8$, and whether it is a primary order or a modulation induced by coexisting charge order. An answer is a phase-sensitive or scattering detection of $\Delta_Q$ with its correlation length, or a bound that excludes it.
What would settle it
A bulk probe (x-ray or neutron scattering, or c-axis Josephson coupling in La2-xBaxCuO4) showing long-range $\Delta_Q$ order with a correlation length exceeding that of the coexisting charge order.
Status in the literature
Scanned Josephson tunneling found a $4a0$ pair-density modulation in Bi2Sr2CaCu2O8+x at zero field (2016) and field-induced $8a0$ modulations near vortex cores (2019); whether a primary long-range pair density wave exists in the bulk is not established.