Collective modes in 2 dimensional fermionic superfluid near Pomeranchuk instability

Kelly Reidy

John B. Ketterson, Shenian N. Song

Wei-Han Hsiao

In this work, we utilize semiclassical kinetic equations to investigate the order parameter collective modes of a class of two-dimensional superfluids. Extending the known results for $p$-wave superfluids, we show that for any chiral ground state of angular momentum $L\ensuremath{\ge}1$, there exists a subgap mode with a mass $\sqrt{2}\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}$ in the BCS limit, where $\mathrm{\ensuremath{\Delta}}$ is the magnitude of the ground-state gap. We determine the most significant Landau parameter that contributes to the mass renormalization and show explicitly that the renormalized modes become massless at the Pomeranchuk instability of the fermion vacuum. Particularly for $L=1$, we propose a continuous field theory to include the Fermi liquid effect in a quadrupolar channel and produce the same result under consistent approximations. They provide potential diagnostics for distinguishing two-dimensional chiral ground states of different angular momenta with the order parameter collective modes and reveal another low-energy degree of freedom near the nematic transition.

Victor Nikolaevich Popov

Avraham Klein, Dmitrii L. Maslov, Lev P. Pitaevskii +1 more

This paper studies zero-sound collective modes in a two-dimensional (2D) Fermi liquid near a spontaneous instability around a Fermi surface deformation. The results show that the zero-sound mode softens at the instability and that these modes are different from their 3D counterparts. The authors explain these features as the onset of a non-trivial topological structure of the Riemann surface harboring the singularities of the dynamic susceptibility.

Michael McNeil Forbes, Aurel Bulgac, Gabriel Wlazłowski