# Electrodynamics on Fermi Cyclides in Nodal Line Semimetals

## TL;DR

This paper investigates the optical conductivity of nodal line semimetals, revealing complex spectral features influenced by Fermi surface geometry and energy dispersion, supported by numerical calculations.

## Contribution

It introduces a scaling framework based on Dupin cyclide Fermi surfaces to understand the frequency-dependent conductivity in NLSMs.

## Key findings

- Identification of distinct frequency regimes with specific scaling laws
- Numerical validation of the scaling rules for optical conductivity
- Insights into the role of Fermi surface geometry in electronic responses

## Abstract

We study the frequency-dependent conductivity of nodal line semimetals (NLSMs), focusing on the effects of carrier density and energy dispersion on the nodal line. We find that the low-frequency conductivity has a rich spectral structure which can be understood using scaling rules derived from the geometry of their Dupin cyclide Fermi surfaces. We identify different frequency regimes, find scaling rules for the optical conductivity in each, and demonstrate them with numerical calculations of the inter- and intraband contributions to the optical conductivity using a low-energy model for a generic NLSM.