Optical conductivity of the threefold Hopf semimetal

TL;DR

This paper theoretically investigates the optical conductivity of threefold Hopf semimetals, revealing anisotropic responses to polarized light, including frequency-dependent conductivity and polarization-sensitive Hall currents, which are robust against temperature and disorder.

Contribution

It introduces a minimal model to analyze the anisotropic optical responses of threefold Hopf semimetals, highlighting the role of symmetry and Berry dipole in their optical properties.

Findings

Optical conductivity exhibits anisotropic dependence on polarization angle.

Longitudinal optical conductivity is linear in frequency with step-like features.

Polarization orientation affects the number of steps and Hall current presence.

Abstract

A multifold Hopf semimetal is a topological point node semimetal possessing an anisotropy in the internal electronic structure, e.g., the dipole structure of the Berry curvature. In this paper, the unique features of threefold Hopf semimetals in terms of the optical conductivity are theoretically investigated with a minimal theoretical model by using linear response theory for a linearly polarized photon. The frequency spectrum of the optical conductivity shows an anisotropic dependence on the polarization angle of the incident photon even if the electronic band structure is completely isotropic. The longitudinal optical conductivity linearly depends on the photon frequency and possesses step-like changes in the frequency spectrum. The anisotropic electronic structure has a varying the number of steps with the orientation of the photon polarization axis. We reveal that the anisotropy is attributed to symmetries preserving the point node in threefold Hopf semimetals. The linearly polarized photon also induces a Hall current but it vanishes with the photon polarization axis parallel to the Berry dipole axis. The numerical calculations show that these characteristic features can be observed even with a non-zero temperature and disorder.