Hidden and mirage collective modes in two dimensional Fermi liquids

The longstanding view of the zero sound (ZS) mode in a Fermi liquid is that for repulsive interaction it resides outside the particle-hole continuum and gives a sharp peak in susceptibility, while for attractive interaction it is a resonance inside the continuum. The authors argue that in a clean two-dimensional Fermi liquid there exist two additional types of ZS: hidden and mirage modes. A hidden mode resides outside the continuum already for attractive interaction; it does not appear as a sharp peak in susceptibility but controls the long-time transient response and can be identified in pump-probe experiments. A mirage mode emerges for sufficiently strong repulsion; it does not correspond to a true pole, yet it yields a peak in the particle-hole susceptibility whose width exceeds the single-particle scattering rate. These features are traced to the algebraic branch points at ω = ±vF q in 2D, which create a two-sheet Riemann surface for χ(q,ω) and allow poles to move between physical and unphysical sheets.

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