What are ARPES features of charge density waves in the phase diagram of high-Tc superconductors? Part of the phase diagram of high-$T_c$ superconductors is charge density waves in the superconducting phase. What are distinctive features of ARPES (Angle-resolved photoemission spectroscopy) for such a phase?
Moreover, there may be pair density waves, which are density waves of Cooper pairs. Are there any distinctive features of ARPES for such a phase, in comparison with other phases?
 A: I'm not an expert in cuprates but I have recently read into the matter of seeing charge order in some transition metal oxides, especially in nickel compounds, and I have done ARPES on semiconductors many years ago. 
A good review reference for ARPES (angle resolved emission) on cuprate superconductors seems to be
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.75.473
Simply speaking, the impact of a charge density wave on ARPES is to simply repeat the bands with a wave vector corresponding to the wave. For example, if you have a charge order of 1/3 the Brillouin zone,  you would see a repetition of the band structure at 1/3 of the zone (as well as 2/3 bc of the brilliouin zone reputation at 1).
So for charge order, you would expect to see a repetition of the cuprate bands at the charge ordering vector. It seems so far, no one has ever seen such repetitions in cuprate superconductors. 
For a density wave of the cooper pairs, I don't fully understand the circumstances, so I assume this just means a spatial modulation of the superconducting gap. In that case you would see suppression of the superconducting gap at certain wavevectors of the fermi surface corresponding to the periodicity of that modulation. If that vector does not lie on the Fermi surface I'm not sure you would see this effect at all. In any case, it seems like this effect has not been seen either. 
A: What ARPES measures is the electron energy dispersion (filled), from which you can see gaps. However, ARPES itself does not directly tell you the nature of those gaps. But indirectly you might get some hint about the nature of that gap from, say, the evolution of the gap as a function of wavevector k, magnetic field, temperature, or chemical doping etc. For example, the following theoretical paper discusses some ARPES data feature that seems to agree with the PDW prediction while it is inconsistent with a CDW gap. The distinction comes from that the way these two kinds of gaps open up in the k-space are quite different. What are other possible distinctive features of the PDW order in ARPES? We do not know so far. ARPES is unlikely to be the smoking gun experiment for PDW if PDW is relevant to the phase diagram of copper based hight-Tc superconductor at all. 
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.031017
