Symmetry-Broken Ground State and Phonon-Mediated Superconductivity in Kagome CsV_{3}Sb_{5}

The newly discovered family of nonmagnetic kagome metals AV_{3}Sb_{5} (A=K, Rb, or Cs) provides a unique platform for exploring the interplay between charge-density wave (CDW) order, superconductivity, nontrivial topology, and spontaneous time-reversal symmetry breaking. Although characterizing the CDW phase is essential for understanding and modeling these exotic phenomena, its nature remains unresolved. In this Letter, we employ first-principles free-energy calculations, accounting for both ionic kinetic energy and anharmonic effects, to resolve the atomistic phase diagram of CsV_{3}Sb_{5} and its charge ordering structure. Our results uncover that the CDW ground state is formed by reconstructed vanadium kagome layers in a triangular-hexagonal pattern, featuring energetically degenerate different stacking orders. This accounts for the various out-of-plane modulations observed experimentally and supports the coexistence of multiple domains. The discovered symmetry-broken ground state is consistent with the absence of any electronic anisotropy in transport experiments. By combining anharmonic phonons with the calculation of electron-phonon matrix elements, we predict a superconducting critical temperature for the CDW phase in agreement with experiments showing that superconductivity is phonon mediated. These findings not only resolve a long-standing structural puzzle, but also clarify the impact of the CDW in superconductivity, highlighting its fundamental importance in shaping the low-temperature quantum phase diagram of kagome metals.