Phenomenological BCS theory of the high-$T_c$ cuprates

A BCS model characterized by a phenomenological pair potential with on-site ($V_0$), nearest ($V_1$), and next nearest ($V_2$) neighbour coupling constants, and an empirical quasiparticle dispersion taken from angle-resolved photoemission spectra is considered. The model can consistently explain the experimental data concerning the pair state of the hole doped cuprates. Three ingredients are required to make the interpretation possible: the existence of flat bands, a very small effective on-site repulsion, and a slightly dominating effective nnn attraction $V_2$ of the order of 60-80meV with a ratio $V_2/V_1 \approx 1.5$.