Mirage and hidden 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 two exotic types of zero-sound collective modes: sharp propagating “hidden” modes that cannot be detected by spectroscopy and “mirage” modes that appear as sharp peaks in spectroscopy but don’t determine the Fermi liquid’s response. I will discuss how these features are associated with the existence of a two-sheet Riemann surface defined by the dynamical susceptibility χ(q,ω). The hidden modes reside below the branch cut gluing the sheets, and the illusory modes reside on an unphysical sheet of the Riemann surface. Although neither the existence of a hidden mode, nor the illusory nature of a mirage mode, appear in spectroscopic probes, both can be readily identified in time-dependent measurements in pump-probe configurations.