Different doping from apical and planar oxygen vacancies in Ba$_{2}$CuO$_{4-δ}$ and La$_{2}$CuO$_{4-δ}$

First principles band-structure calculations for large supercells of Ba$_{2}$CuO$_{4-δ}$ and La$_{2}$CuO$_{4-δ}$ with different distributions and concentrations of oxygen vacancies show that the effective doping on copper sites strongly depends on where the vacancy is located. A vacancy within the Cu layer produces a weak doping effect while a vacancy located at an apical oxygen site acts as a stronger electron dopant on the copper layers and gradually brings the electronic structure close to that of La$_{2-x}$Sr$_x$CuO$_{4}$. These effects are robust and only depend marginally on lattice distortions. Our results show that deoxygenation can reduce the effect of traditional La/Sr or La/Nd substitutions. Our study clearly identifies location of the dopant in the crystal structure as an important factor in doping of the cuprate planes.

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