Mechanisms for superconductivity, density wave, and excitonic order in kagome metals

The recent discovery of superconducting kagome metals AV₃Sb₅ (A= K, Rb, Cs) have provided an exciting example of quasi-two-dimensional materials exhibiting unconventional superconductivity, a topologically non-trivial normal state, and novel competing ground states - with density wave order and signatures of time-reversal symmetry breaking above T_c. Inspired by these developments, this talk will describe theoretical approaches to superconductivity in kagome metals. First, we describe a theory reliant on approximately nested portions of the Fermi surface. Considering a stack of weakly-coupled two-dimensional layers at slightly displaced carrier densities, we find weak interlayer coupling gives rise to a chiral excitonic instability alongside density wave order and superconductivity. The perturbative RG method is used to analyze the interplay between superconductivity and competing orders. Second, we describe an approach which relies on the unnested Dirac pockets. The Berry phase of the Dirac points leads to a destructive interference effect, whereby a paired state of electrons with momenta k and -k partially cancels the Coulomb repulsion, making it energetically preferable to form Cooper pairs. The resulting superconducting state is spatially modulated, and possesses higher-order topology with Majorana corner modes. Connections with experiments on AV₃Sb₅ are discussed.