Time-reversal symmetry-breaking, nematicity, and charge-density wave order in the AV₃Sb₅ kagome metals

The family of metallic kagome compounds AV₃Sb₅ (A=K, Rb, Cs) was recently discovered to exhibit both superconductivity and charge-density wave (CDW) order. Density functional theory shows that phonon modes from both the M- and L-points in the Brillouin zone become unstable near the CDW transition. Low-energy models also support closely competing real and imaginary CDW orders. Motivated by these results, we construct a Landau free energy for the coupled CDW orders. In addition to the usual biquadratic coupling, we also find unusual trilinear and quadrilinear couplings. As a result, the phase diagram exhibits a rich landscape with multiple novel phenomena appearing due to the mixing of closely competing instabilities. We find both nematic and non-nematic phases that break time-reversal symmetry and that lead to the experimentally observed quadrupling of the unit cell. Interestingly, while the iCDW nematic phase does not exhibit an induced dipole moment, its non-nematic iCDW counterpart does. To provide a guide for scattering experiments we classify the space groups of the stable phases and explore additional experimental signatures that can help pinpoint the precise nature of the charge-ordered phase observed in the kagome metals.