High field charge order across the phase diagram of $YBa_2Cu_3O_y$

In hole-doped cuprates there is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstruction of the Fermi surface. In $YBa_2Cu_3O_y$ charge order emerges in two steps: a 2D order found at zero field and at high temperature inside the pseudogap phase, and a 3D order that is superimposed below the superconducting transition $T_c$ when superconductivity is weakened by a magnetic field. Several issues still need to be addressed such as the effect of disorder, the relationship between those charge orders and their respective impact on the Fermi surface. Here, we report high magnetic field sound velocity measurements of the 3D charge order in underdoped $YBa_2Cu_3O_y$ in a large doping range. We found that the 3D charge order exists over the same doping range as its 2D counterpart, indicating an intimate connection between the two distinct orders. Moreover, we argue that the Fermi surface is reconstructed above the onset temperature of 3D charge order.