Table 1 Model parameters, their physical significance, and experimental/theoretical justifications.

t

0.3 eV

Electron hopping integral

Typical for \(\text {CuO}_2\) planes³⁸

\(\omega _D\)

0.07 eV

Debye frequency (optical phonons)

Oxygen modes in cuprates¹²

\(\omega '_D\)

0.006 eV

Debye frequency (acoustic phonons)

Lattice vibrations from neutron scattering, adjusted to match acoustic dispersion up to  6 meV at BZ boundary^13,43,44,45

g

0.35 eV

Linear electron-phonon coupling strength (optical)

ARPES and neutron scattering, adjusted for higher Tc^13,46

\(g'\)

0.08 eV

Linear electron-phonon coupling strength (acoustic)

Extended for multi-mode effects³⁰

\(\gamma\)

0.1 eV

Quadratic electron-phonon coupling strength

Quantum bipolaron models¹⁶

U

2 eV

On-site Coulomb repulsion

Hubbard model for cuprates⁵

N(0)

1 \(\text {eV}^{-1}\)

Density of states at Fermi level

Standard for 2D cuprates⁴⁷

\(\eta\)

\(10^{-4}\) eV

Damping factor for numerical stability

Ensures convergence³⁹

\(x_{\text {opt}}\)

0.16

Optimal doping level

Typical for cuprates like \(\text {La}_{2-x}\text {Sr}_{x}\text {CuO}_4\)⁴⁸