  Threefold Hopf semimetals are a novel type of topological semimetals that
possess an internal anisotropy characterized by a dipolar structure of the
Berry curvature and an isotropic energy band structure consisting of a Dirac
cone and a flat band. In this study, we theoretically investigate the impact of
internal anisotropy on plasmons in threefold Hopf semimetals using random-phase
approximation. In contrast to the classical intuition that isotropy of the
energy band dispersion leads to isotropic plasmons in the classical regime
(i.e., in the wavelength limit), we find that plasmons in threefold Hopf
semimetals exhibit notable anisotropy even in the long-wavelength limit. We
derive an explicit analytical form of the long-wavelength plasmon frequency,
and numerically demonstrate the validity of our results in a wide range of
situations. Our work reveals that the anisotropy of long-wavelength plasmons
can reach 25%, making it experimentally observable.
