The nature of the superconducting pairing state in the pristine phase of the compressed kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ under pressure is studied by the Migdal-Eliashberg formalism and density-functional theory calculations. We find that the superconducting gap distribution driven by electron-phonon coupling is anisotropic and nodeless. It is revealed that the V $3d$ and Sb $5p$ orbitals forming the four Fermi surface sheets are strongly coupled to the V-V bond-stretching and V-Sb bond-bending phonon modes. The resultant superconducting gaps associated with V $3d_{xy,x^2-y^2,z^2}$ and $3d_{xz,yz}$ orbitals is larger in their average magnitude and more widely spread compared to that associated with the Sb $5p_z$ orbital. Meanwhile, we find that unconventional superconductivity driven by electron correlation effects is unlikely because the saddle points at the $M$ point near the Fermi level do not generate van Hove singularities in the total density of states. Our findings demonstrate that the superconductivity of compressed ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ can be explained by the anisotropic multiband pairing mechanism with conventional phonon-mediated $s$-wave symmetry, evidenced by recent experimental observations at ambient pressure and under pressure.

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• Pairing mechanisms
• Superconducting gap
• Superconductivity