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First-principles density functional theory calculations are performed tounderstand the electronic structure and interaction parameters for recentlydiscovered superconducting Kagome metal CsV$_3$Sb$_5$. A systematic analysis ofthe tight-binding parameters based on maximally localized Wannier functionmethod demonstrates that the out-of-plane Sb$^{\rm out}$-$p$ orbital is a keyelement in complete description of the three Van Hove singularity structuresknown in this material at $M$ point near the Fermi level. Further, thecorrelation strengths are also largely determined by Sb$^{\rm out}$-$p$ states.Based on constrained random phase approximation, we find that on-site andinter-site interaction parameter are both significantly affected by thescreening effect of Sb$^{\rm out}$-$p$ orbitals. As the role of this previouslyunnoticed orbital state can be tuned or controlled by out-of-plane latticeparameters, we examine the electronic structure and particularly the evolutionof Van Hove singularity points as a function of strain and pressure, which canserve as useful knobs to control the material properties.

physical review. b./physical review. b

Crucial role of out-of-plane Sb-$p$ orbitals in Van Hove singularity  formation and electronic correlation for superconducting Kagome metal  CsV$_3$Sb$_5$