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The three-band \emph{d-p} model is investigated by means of VariationalMonte-Carlo (VMC) method with the BCS-like wave-function supplemented by theGutzwiller and Jastrow correlators. The VMC optimization leads to $d$-$wave$superconducting state with a characteristic dome-like shape of the orderparameter for hole doping $\delta \lesssim 0.4$, in a good agreement with theexperimental observations. Also, the off-diagonal pair-pair correlationfunctions, calculated within VMC, vindicates the results obtained very recentlywithin the diagrammatic expansion of the Gutzwiller wave function method(DE-GWF) [cf. Phys. Rev. B \textbf{99}, 104511 (2019)]. Subsequently, thenature of the $d$-$wave$ pairing is investigated by means of recently proposed\emph{minimal-size real-space d-wave pairing operators} [Phys. Rev. B\textbf{100}, 214502 (2019)]. An emergence of the long-range superconductingordering for both $d$ and $p$ orbitals is reported by analysing thecorresponding off-diagonal pair-pair correlation functions. The dominantcharacter of \emph{d-wave} pairing on $d$ orbitals is confirmed. Additionally,the trial wave-function is used to investigate the magnetic properties of thesystem. The analysis of spin-spin correlation functions is carried out andshows antiferromagnetic $\mathbf{q}=(\pi,\pi)$, short-range order, as expected.For the sake of completeness, the charge gap has been estimated, which for theparent compound takes the value $\Delta_{CG}\approx1.78\pm0.51\text{ eV}$, andagrees with values reported experimentally for the cuprates.

Superconducting properties of the hole-doped three-band \emph{d-p} model studied with minimal-size real-space \emph{d}-wave pairing operators