Phonon-mediated s -wave superconductivity in the kagome metal CsV3Sb5 under pressure

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 $3{d}_{xy,{x}^{2}\ensuremath{-}{y}^{2},{z}^{2}}$ and $3{d}_{xz,yz}$ orbitals is larger in their average magnitude and more widely spread compared to that associated with the Sb $5{p}_{z}$ 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.