Title: Calculated Unconventional Superconductivity via Charge Fluctuations in Kagome Metal CsV3Sb5

Abstract: Electrons on Kagome lattice exhibit a wealth of features including Dirac points, van Hove singularities and flatbands. When the Fermi level is placed at the van Hove saddle point, the Fermi surface is perfectly nested and a rich variety of electronic instabilities is known to occur. The material realization of such scenario is a recently discovered Kagome system CsV3Sb5 whose superconductivity near charge-density wave instability at low temperatures points to an unconventional, non-electron-phonon, pairing mechanism. Here we use a recently developed combination of density functional theory with momentum and frequency-resolved self-energies deduced from the so-called fluctuational-exchange-type random phase approximation to study charge fluctuation mediated pairing tendencies in CsV3Sb5. Based on our numerical diagonalization of the BCS gap equation, two competing solutions emerge from these calculations with A_{1g} (anisotropic s-wave-like) and B_{2g} (d_{x2-y2},d_{xy}-like) symmetries of the superconducting order parameter. Our evaluated Eliashberg spectral functions {\alpha}2F({\omega}) are purely due to electronic correlations; they were found to be strongly peaked in the vicinity of frequency 7 meV that sets the scale of charge fluctuations. The superconducting coupling constants for the leading pairing channels are estimated as a function of the nearest neighbor Coulomb interaction V, a well-known prime parameter of the extended Hubbard model. They were found in the range of 0.2-0.4 depending on V. We evaluate the superconducting T_{c} close to the values that are observed experimentally that point to the charge fluctuations to provide a substantial contribution to the pairing mechanism in CsV3Sb5.