Superconducting dome with extended <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>s</mml:mi></mml:math> -wave pairing symmetry in the heavily hole-overdoped copper-oxide planes

We analyze the two-orbital (with $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals) analogue of $t$-$J$-$U$ model as applied to description copper-oxide monolayer deposited on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ substrate (CuO$_2$/BSCCO). show, that an $extended$ $s$-$wave$ superconducting dome appears in heavily hole overdoped regime model, with dominant contribution pairing coming from orbitals. Also, lower critical doping for appearance SC state concurs Lifshitz Transition after which hole-like Fermi pockets are created around $M$ points Brillouin zone. The obtained results accord recent experimental result [cf. Y. Zhong et al., Sci. Bull. 61, 1239 (2016)]. An analogous two-band is also analyzed context Ba$_2$CuO$_{4-y}$ bulk compound, where hole-overdoped situation believed be reached W. M. Li al. PNAS 116, 12156 (2019)]. As we a two structure can realized such system $d$- symmetries gap corresponding low hole-doping cases, respectively.