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Fermi arcs and pseudogap emerging from dimensional crossover at the Fermi surface in La$_{2-x}$Sr$_x$CuO$_4$

The doping mechanism and realistic Fermi surface (FS) evolution of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) are modelled within an extensive ab-initio framework including advanced band-unfolding techniques. We show that ordinary Kohn-Sham DFT+U can reproduce the observed metal-insulator transition, when not restricted to the paramagnetic solution space. Arcs are self-doped by orbital charge transfer within the Cu-O planes, while the introduced Sr charge is strongly localized. Arc protection and the inadequacy of the rigid-band picture are consequences of a rapid change in orbital symmetry at the Fermi energy: the material undergoes a dimensional crossover along the Fermi surface, between the nodal (2D) and antinodal (3D) regions. In LSCO, this crossover accounts for FS arcs, the antinodal pseudogap, and insulating behavior in $c$-axis conductivity, all ubiquitous phenomena in high-T$_c$ cuprates. Ligand Coulomb integrals involving out-of-plane sites are principally responsible for the most striking effects observed by ARPES in LSCO.