Abstract

All previous cuprate superconductors display a set of common features: (i) vicinity to a Cu $3{d}^{9}$ configuration; (ii) separated ${\mathrm{CuO}}_{2}$ planes; and (iii) superconductivity for doping $\ensuremath{\delta}\ensuremath{\sim}0.1--0.3$. Recently, Li et al. [Proc. Natl. Acad. Sci. USA 116, 12156 (2019)] challenged this picture by discovering ``highly overdoped'' superconducting ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+y}$. Using density-functional theory plus dynamical mean-field theory, we reveal a bilayer structure of ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3.2}$ of alternating quasi-two-dimensional (2D) and quasi-one-dimensional (1D) character. Correlations tune an interlayer self-doping leading to an almost half-filled, strongly nested, quasi-1D ${d}_{{b}^{2}\ensuremath{-}{c}^{2}}$ band, which is prone to strong antiferromagnetic fluctuations, possibly at the origin of superconductivity in ${\mathrm{Ba}}_{2}{\mathrm{CuO}}_{3+y}$.

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