Negative refraction and rotons in the relativistic Bose gas

TL;DR

This paper explores how a relativistic Bose gas affects electromagnetic wave propagation, revealing negative refraction and roton-like features in the plasma's response, with implications for novel optical materials.

Contribution

It introduces a detailed analysis of electromagnetic responses in a relativistic Bose gas, demonstrating negative refraction and roton phenomena using quantum electrodynamics at finite temperature.

Findings

The gas exhibits negative effective index of refraction below the plasmon frequency.

A roton-like local minimum appears in the plasmon dispersion in the condensed phase.

The roton feature disappears at the phase transition temperature.

Abstract

We investigate the dispersion of a classical electromagnetic field in a relativistic ideal gas of charged bosons using scalar quantum electrodynamics at finite temperature and charge density. We derive the effective electromagnetic responses and the electromagnetic propagation modes that characterize the gas as a left-handed material with negative effective index of refraction $n_{\rm eff}=-1$ below the transverse plasmon frequency. In the condensed phase, we show that the longitudinal plasmon dispersion relation exhibits a roton-type local minimum that disappears at the transition temperature.