In this thesis, we utilize semi-classical 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 ≥ 1, there exists a subgap mode with a mass (√2) ∆ in the BCS limit, where ∆ 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 the 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.




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