Plasmons in three-dimensional superconductors

We study the plasma branch of an homogeneous three-dimensional electron gas in an s-wave superconducting state. Although a sum rule guarantees that the departure of the plasma branch always coincides with the plasma frequency cop, the dispersion and lifetime of plasmons is strongly affected by the presence of the pair condensate, especially when cop is close to the pair-breaking threshold 2A. When cop is between 1.7A and 2A, the level repulsion is strong enough to give the plasma branch an anomalous, downward dispersion and a dispersion minimum strictly lower than cop. Then for cop > 2A, plasmons damp out in pair-breaking excitations, acquiring a small damping rate at zero temperature, which we compute in a non-perturbative way. Finally, the density-density response function displays a resonance near 2A (not to be confused with the amplitude mode), which can beat with the main plasma resonance, and subsists for cop large compared to A, thereby distinguishing charged from neutral condensates.

Automated summary

We study the plasma branch of a homogeneous three-dimensional electron gas in an s-wave superconducting state. The dispersion and lifetime of plasmons are affected by the presence of the pair condensate. When the plasma frequency is close to the pair-breaking threshold, the plasma branch displays anomalous downward dispersion and a dispersion minimum lower than the plasma frequency. At high plasma frequencies, the plasmons damp out in pair-breaking excitations, acquiring a small damping rate at zero temperature.