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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 $γ$ exceeds plasmon resonance frequency. Resonances feature a recurrent behavior as $γ$ increases, first broadening and then narrowing and acquiring asymmetric non-Lorentzian lineshapes with power-law tails extending into the tachyon continuum $ω>ck$. This unusual behavior can be linked to the properties of tachyon poles located beneath $ω>ck$ branch cuts in the complex $ω$ plane: as $γ$ grows, tachyon poles approach the light cone and hybridize with plasmons. Narrow resonances persisting for $γ>ω$, along with the unusual density and temperature dependence of resonance frequencies, provide clear signatures of the tachyon regime.