Hidden one-dimensional, strongly nested, and almost half-filled Fermi surface in Ba2CuO3+y superconductors

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 ${\mathrm{Ba}}₂{\mathrm{CuO}}_3+y$.