Charge density waves and electronic properties of superconducting kagome metals

Kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, and Cs) exhibit intriguing superconductivity below $0.9 \sim 2.5 $ K, a charge density wave (CDW) transition around $80\sim 100 $ K, and $\mathbb{Z}_{2}$ topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the $2\times2\times2$ CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial $\mathbb{Z}_{2}$-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity $T_c$ in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.