# Hyperbolic Dispersion in Chiral Molecules

## TL;DR

This paper theoretically demonstrates hyperbolic dispersion in Möbius molecules caused by intra-band transitions, leading to broad negative refraction bandwidths shifting from ultraviolet to visible frequencies.

## Contribution

It reveals hyperbolic dispersion due to intra-band transitions in Möbius molecules and quantifies the negative refraction bandwidth, expanding potential applications.

## Key findings

- Hyperbolic dispersion induced by intra-band transitions.
- Negative refraction bandwidth of 0.1952 eV for H-polarized light.
- Shift of negative refraction frequency domain from ultraviolet to visible.

## Abstract

We theoretically investigate the intra-band transitions in M\"{o}bius molecules. Due to the weak magnetic response, the relative permittivity is significantly modified by the presence of the medium while the relative permeability is not. We show that there is hyperbolic dispersion relation induced by the intra-band transitions because one of the eigen-values of permittivity possesses a different sign from the other two, while all three eigen-values of permeability are positive. We further demonstrate that the bandwidth of negative refraction is 0.1952~eV for the $H$-polarized incident light, which is broader than the ones for inter-band transitions by 3 orders of magnitude. Moreover, the frequency domain has been shifted from ultra-violet to visible domain. Although there is negative refraction for the $E$-polarized incident light, the bandwidth is much narrower and depends on the incident angle.