The longstanding view of the zero sound mode in a Fermi liquid is that for repulsive interaction it resides outside the particle-hole continuum and gives rise to a sharp peak in the corresponding susceptibility, while for attractive interaction it is a resonance inside the particle-hole continuum. We argue that in a two-dimensional Fermi liquid there exist two additional types of zero sound: “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 susceptibility, but determines the long-time transient response of a Fermi liquid and can be identified in pump-probe experiments. A mirage mode emerges for strong enough repulsion. Unlike the conventional zero sound, it does not correspond to a true pole, yet it gives rise to a peak in the particle-hole susceptibility. It can be detected by measuring the width of the peak, which for a mirage mode is larger than the single-particle scattering rate.
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We thank M.H. Christensen, A. Kamenev, L. Levitov and L.P. Pitaevskii for stimulating discussions. This work was supported by the NSF DMR-1834856 (A.K. and A.V.C.), NSF-DMR-1720816 (D.L.M.), and UF DSP Opportunity Fund OR-DRPD-ROF2017 (D.L.M.). A. V.C. is thankful to the Aspen Center for Physics (A.S.P.) for hospitality during the completion of this work. A.S.P. is supported by National Science Foundation grant PHY-1607611.