Hidden and mirage collective modes in two dimensional Fermi liquids

I will show that two-particle correlation functions in 2D Fermi liquids have a nontrivial topological structure. The structure manifests itself in unconventional zero-sound collective modes: “hidden” and “mirage” modes. A hidden mode resides outside the particle-hole continuum already for attractive interaction. It does not appear as a sharp peak in the dynamical susceptibility χ(q,ω), yet determines the long-time transient response of a Fermi liquid. A mirage mode emerges for strong enough repulsion. Unlike the conventional zero sound, it does not correspond to a pole of χ(q,ω), yet gives rise to a peak in the particle-hole susceptibility. I will discuss how these features are associated with the existence of a two-sheet Riemann surface defined by χ(q,ω). The hidden modes reside below the branch cut gluing the sheets, and the mirage modes reside on an unphysical sheet of the Riemann surface.