Charge density wave order near the non-superconductor to superconductor phase transition in YBa$_2$Cu$_3$O$_{6+x}$

Using resonant x-ray scattering, we extend previous studies of the doping dependence of charge density wave (CDW) order in YBa$_2$Cu$_3$O$_{6+x}$ (YBCO) to the heavily underdoped regime. We find that CDW order persists down to low doping ($x=0.335, p = 0.06$), close to the non-superconductor to superconductor phase transition and within a regime where static incommensurate spin density wave (SDW) order has been observed. Notably, at this low doping, the CDW order is unidirectional, propagating along the $b$ axis but not along the $a$ axis. Moreover, we identify a reduction of the $a$-axis correlation length, $\xi_a$, relative to the $b$ axis correlation length, $\xi_b$, at low doping, indicative of a unidirectional character to CDW order in YBCO.