Symmetry of Charge Density Waves and Response Tensors in AV₃Sb₅ Kagome Metals

Space group symmetries and multipole moments allowed by them can be used to predict the macroscopic response of ferroic materials, including ferroelectrics, (anti-)ferromagnets, and multiferroics. In this talk, we apply similar ideas to charge density wave materials with time-reversal symmetry breaking imaginary charge density wave phases. The AV₃Sb₅ (A=K, Rb, Cs) Kagome metals undergo multiple charge density wave transitions in addition to hosting superconducting and topological phases.This charge ordering behavior may involve both bond distortions ( "real" charge density waves) and time-reversal symmetry breaking loop currents. In this talk, we classify different charge density wave phases using magnetic space groups and their representations. By studying the allowed elements of various macroscopic response tensors, including piezomagnetic and magneto-optical tensors, we lay out experimental pathways to pin down the symmetry of the charge density wave phases in these systems and possibly observe novel nonreciprocal optical effects. We also comment on the implications of the possible Kerr rotation in Kagome metals.