  Many issues concerning the origin of high-temperature superconductivity (HTS)
are still under debate. For example, how the magnetic ordering varies with
doping and its relationship with the superconducting temperature; and why the
maximal Tc always occurs near the quantum critical point. In this paper, taking
hole-doped La2CuO4 as a classical example, we employ the first-principles band
structure and total energy calculations and Monte Carlo simulations to explore
how the symmetry-breaking magnetic ground state evolves with hole doping and
the origin of a dome-shaped superconductivity region in the phase diagram. We
demonstrate that the local antiferromagnetic ordering and doping play key roles
in determining the electron-phonon coupling, thus Tc. Initially, the La2CuO4
possesses a checkerboard local antiferromagnetic ground state. As the hole
doping increases, Tc increases with the increase of the density of states at
the Fermi surface. But as the doping increases further, the strength of the
antiferromagnetic interaction weakens. At the critical doping level, a magnetic
phase transition occurs that reduces the local antiferromagnetism-assisted
electron-phonon coupling, thus diminishing the Tc. The superconductivity
disappears in the heavily overdoped region when the antiferromagnetic ordering
disappears. These observations could account for why cuprates have a
dome-shaped superconductivity region in the phase diagram. Our study, thus,
contributes to a fundamental understanding of the correlation between doping,
local magnetic ordering, and superconductivity of HTS.
