Plasmon resonances and tachyon ghost modes in highly conducting sheets

Plasmon-polariton modes in two-dimensional electron gases have a dual field-matter nature that endows them with unusual properties when electrical conductivity exceeds a certain threshold set by the speed of light. In this regime plasmons display an interesting relation with tachyons, the hypothetical faster-than-light particles. While not directly observable, tachyons directly impact properties of plasmon modes. Namely, in the ``tachyon'' regime, plasmon resonances remain sharp even when the carrier collision rate $\ensuremath{\gamma}$ exceeds plasmon resonance frequency. Resonances feature a recurrent behavior as $\ensuremath{\gamma}$ increases, first broadening and then narrowing and acquiring asymmetric non-Lorentzian line shapes with power-law tails extending into the tachyon continuum $\ensuremath{\omega}>ck$. This unusual behavior can be linked to the properties of tachyon poles located beneath $\ensuremath{\omega}>ck$ branch cuts in the complex $\ensuremath{\omega}$ plane: as $\ensuremath{\gamma}$ grows, tachyon poles approach the light cone and hybridize with plasmons. Narrow resonances persisting for $\ensuremath{\gamma}>\ensuremath{\omega}$, along with the unusual density and temperature dependence of resonance frequencies, provide clear signatures of the tachyon regime.