This paper challenges the conventional understanding of zero sound (ZS) modes in Fermi liquids, proposing the existence of "hidden" and "mirage" ZS modes in two-dimensional (2D) Fermi liquids. A hidden mode, present even with attractive interactions, doesn't produce a sharp peak in susceptibility but influences long-time transient responses, detectable via pump-probe experiments. A mirage mode, arising from strong repulsion, appears as a peak in susceptibility but isn't a true pole, exhibiting a width exceeding the single-particle scattering rate. These unconventional modes stem from the algebraic non-analyticity of the 2D susceptibility, leading to distinct behavior in time-domain responses.

Avraham Klein, Dmitrii L. Maslov, Andrey V. Chubukov