Fermi Arc Evolution and Doping Mechanism in High-Temperature Superconductors

We calculate realistic Fermi surface (FS) evolution of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) with Sr doping 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 and arc growth, when not restricted to the paramagnetic solution space. We elucidate both arc protection and the inadequacy of the rigid-band picture as 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 and the antinodal pseudogap, otherwise ubiquitous phenomena in high-Tc cuprates. The orbital transition is experimentally confirmed by replacing 4\% of planar Cu in nearly optimally doped YBa$_2$Cu$_{2.97}$Zn$_{0.03}$O$_{6.92}$ powder with $^{67}$Zn isotope, lowering T$_c$ to 57 K. The NQR spectrum of $^{67}$Zn, measured for the first time, shows that each Zn dopand surrounds itself with an insulating cluster. Zn destroys the SC metal by a Coulomb ``domino effect'' which reverts the orbital transition locally and pushes a significant number of surrounding sites back towards the parent-compound configuration.