# Plasmon Resonances and Tachyon Ghost Modes in Highly Conducting Sheets

## TL;DR

This paper explores the unusual properties of plasmon modes in highly conducting sheets, revealing a regime where tachyon-like behavior influences resonance sharpness and lineshapes, with potential experimental signatures.

## Contribution

It introduces the concept of a tachyon regime in plasmon physics, showing how tachyon poles affect resonance properties in highly conducting two-dimensional electron gases.

## Key findings

- Resonances remain sharp even when collision rate exceeds plasmon frequency.
- Resonance lineshapes become asymmetric with power-law tails in the tachyon regime.
- Resonance behavior depends on density and temperature, indicating tachyon influence.

## Abstract

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.