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Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions, a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted 16 years ago. These highly exotic quasiparticles—the semi-Dirac fermions—ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions— $B^{2/3}$scaling of Landau levels—in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal lines extend the band degeneracies from isolated points to lines, loops, or even chains in the momentum space. With calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal lines in ZrSiS. Crossing nodal lines exhibit a continuum absorption spectrum but with singularities that scale as $B^{2/3}$at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal lines and highlights the potential to explore quantum geometry with linear optical responses. Published by the American Physical Society2024 

The modeling of the near-field interaction in the scattering-type scanning near-field optical microscope (s-SNOM) is rapidly advancing, although an accurate yet versatile modeling framework that can be easily adapted to various complex situations is still lacking. In this work, we propose a time-efficient numerical scheme in the quasi-electrostatic limit to capture the tip-sample interaction in the near field. This method considers an extended tip geometry, which is a significant advantage compared to the previously reported method based on the point-dipole approximation. Using this formalism, we investigate, among others, nontrivial questions such as uniaxial and biaxial anisotropy in the near-field interaction, the relationship between various experimental parameters (e.g. tip radius, tapping amplitude, etc.), and the tip-dependent spatial resolution. The demonstrated method further sheds light on the understanding of the contrast mechanism in s-SNOM imaging and spectroscopy, while also representing a valuable platform for future quantitative analysis of the experimental observations. 

Nodal-line metals allow hyperbolic infrared waveguiding through the bulk with band structure–engineered loss reduction.