# Dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi

## TL;DR

This paper studies the dynamical conductivity of CoSi, a multiply-degenerate point-nodal semimetal, revealing how its unique band structure and chiral fermionic states influence its optical response, especially a characteristic dip at low photon energies.

## Contribution

It provides the first-principles calculation of CoSi's dynamical conductivity, linking spectral features to the chiral fermion states and their transition prohibitions, highlighting differences from Dirac and Weyl semimetals.

## Key findings

- Dynamical conductivity shows a characteristic spectrum related to band structure.
- A dip in low photon-energy conductivity is due to chiral fermion transition restrictions.
- Chirality prohibits certain electronic transitions, affecting optical properties.

## Abstract

We investigate the dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi. In the semimetal, the band structure holds point nodes at the $\Gamma$ and R points in the Brillouin zone and more than three bands touch at the nodes. Around the nodes, electronic states are predicted to be described as the multifold chiral fermion, a new class of fermion. We show that the dynamical conductivity exhibits a characteristic spectrum corresponding to the band structure and the chiral fermionic states. The dynamical conductivity of CoSi is calculated as a function of photon energy by using the first-principles band calculation and linear response theory. We show that a dip structure in the low photon-energy region is attributed to not only the band structure but also the chirality of electronic states. The chirality leads to the prohibition of transition between the lower and upper bands of threefold chiral fermion and thus the transition between the middle and lower bands is relevant to the dynamical conductivity. This transition property is different from the Dirac and Weyl semimetals, the other point-nodal semimetals, where the excitation between the upper and lower bands is relevant to the dynamical conductivity. We discuss the relation between the prohibition and the dip structure by using an effective Hamiltonian describing threefold chiral fermion.