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