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.
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