Reply to 'Comment on 'Anisotropic Scattering Caused by Apical Oxygen Vacancies in Thin Films of Overdoped High Temperature Cuprate Superconductors''

In our recent work [Phys. Rev. Lett. 128, 137001 (2002)], we proposed that the apical oxygen vacancies act as anisotropic scattering impurities. Within the Born approximation, this leads to a quasi-particle scattering rate that is maximal (zero) in the antinodal (nodal) direction. This unique angular dependence provides a straightforward mechanism for some puzzling experimental results in overdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) films regarding the superfluid density $\rho_s$ and optical conductivity $\sigma_1$. In a recent comment by H. U. Ozdemir et al. [arXiv:2206.01301], the importance of the nature of the impurity scattering is re-emphasized, but some challenges to our picture are raised: that we did not consider the change of the electrostatic potential for in-plane electrons once the apical oxygen is missing, the change of Fermi surface topology as the van Hove point is passed, self-energy corrections caused by d-wave pairing, and vertex corrections caused by forward scattering. These concerns are interesting but are either irrelevant or further enhances our conclusions. We discuss these points one by one in this reply.