2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/17382A theory for spin and lattice couplings to the electronic states in high-T$_C$ oxides is presented, with HgBa$_2$CuO$_4$ as an example. A simple analytical model suggests that the barrel band is sensitive to potential perturbations with long-range Fourier components, and that gaps can be opened at the Fermi energy. This is confirmed in self-consistent band calculations for modulations in elongated supercells, where spin waves and phonon coupling compete for equal q-vectors. It is argued that the wavelengths of spin-wave modulations and of the phonon modes with large coupling, depend on the doping. This mechanism supports the idea that pseudogaps are caused by stripe like spin-modulations in underdoped systems, while superconductivity is attributed to enhanced electron-phonon coupling for long wavelength phonons.(3 figures)SuperconductivityMaterials Sciencetext