Correlated electronic structure of the high-temperature superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Ba</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>CuO</mml:mi> <mml:mrow> <mml:

Cuprate superconductors have attracted extensive attention due to high critical temperatures. Conventional cuprates typically contain perfect ${\mathrm{CuO}}_{2}$ planes, which are considered as a key factor to superconductivity since the superconductivity takes place in them. However, in ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ with $\ensuremath{\delta}=0.2$ and O-depleted ${\mathrm{CuO}}_{2}$ planes, superconductivity still arises even with a transition temperature as high as 73 K. Using combined density functional theory and dynamical mean-field theory calculations, we investigated the electronic correlation and electronic structure of ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3.25}$ with alternating quasi-one-dimensional (quasi-1D) CuO planes and O-depleted ${\mathrm{CuO}}_{2}$ planes. We find that although different from the usual cuprates, the Cu atoms are still dominated by a $3{d}^{9}$ configuration and the system is of a new kind of correlated single-orbital physics. The quasi-1D CuO planes, composed of parallel Cu-O chains, are slightly hole-doped quasi-1D Mott insulators, while the O-depleted ${\mathrm{CuO}}_{2}$ planes are more hole doped, with a two-dimensional correlated electronic structure, and may host superconductivity.