"Vestigial excitonic phase in kagome superconductors AV_3Sb_5"
The kagome lattice is a hexagonal network of corner-sharing triangles, and materials based on the kagome motif have long been seen as a natural setting for interesting correlated states of matter. The family of superconducting compounds AV_3Sb_5 (A=K,Rb,Cs) has attracted immense recent attention due to signatures of time-reversal symmetry breaking and nematicity. Yet, controversy has surrounded these observations, with the nature of broken symmetry appearing to depend sensitively on external strain and magnetic fields. Here we unify and explain these seemingly contradictory experiments through the proposal of an unexplored phase of matter — a vestigial excitonic state — which sets in around T_* ~ 40 K. The presence of electron and hole pockets in the bandstructure produces a tendency towards excitonic order -- an interband hybridisation which breaks an approximate U(1) orbital symmetry. We propose the quasi-two-dimensional nature of this system results in such a state melting via phase fluctuations. The application of external fields or strain stabilises a subset of the phase-melted order parameter manifold, referred to as a vestigial state, producing a symmetry-breaking response which depends on the applied probe. We show this phase-melted order parameter manifold reproduces the full set of unusual features of these compounds: observations of piezomagnetism, electric-magnetic chiral anisotropy, unconventional optical rotation, absence of Kerr rotation, unusual elastoresistance response, and a superconducting diode effect. Our proposed vestigial order accounts for probe-dependent symmetry breaking patterns without fine-tuning, providing a unified explanation of seemingly conflicting experiments.