Formation of unusual oxygen vacancy chains in nickelate L a 3 N i 2 O 7

The recently reported nickelate ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ under pressure provides a new platform for exploring unconventional superconductivity. The oxygen vacancies (${\mathrm{V}}_{\mathrm{O}}$'s) are inevitably introduced during the sample preparation, as confirmed by experimental observations. While it is believed the ${\mathrm{V}}_{\mathrm{O}}$'s could play a key role in influencing the superconductivity of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$, their basic structural and electronic properties remain to be clarified. Here, combining the cluster expansion method and first-principles calculations, we successfully identify eight intermediate ground states of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7--x}$ with variable $x$. Contrary to the general assumption of a random distribution, surprisingly, we find the ${\mathrm{V}}_{\mathrm{O}}$'s eventually form exotic one-dimensional chain structures along the in-plane direction in ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7--x}$. These recently discovered ${\mathrm{V}}_{\mathrm{O}}$ chains significantly change the electronic properties with redistributed electrons and altered orbital interactions. The ${d}_{z2}$ orbitals of Ni atoms adjacent to the ${\mathrm{V}}_{\mathrm{O}}$ chain become fully occupied, with a decreased proportion around the Fermi level (${E}_{\mathrm{F}}$). Importantly, a flat ${d}_{x2\ensuremath{-}y2}$ orbital that emerges above ${E}_{\mathrm{F}}$ enhances the transition dipole moment, leading to a prominent peak in optical conductivity perpendicular to the chain, which is ready to be detected experimentally. Furthermore, Wannier downfolding analysis demonstrates significant variations in orbital interactions caused by the ${\mathrm{V}}_{\mathrm{O}}$ chains, particularly the sign changes in intrabilayer ${d}_{z2}$ hopping. Our study provides the benchmark structures of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7--x}$ and develops a deeper insight into the fundamental electronic and optical properties of ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7--x}$.