Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS

Abstract

Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that hosts several Dirac cones that form a Fermi surface with a diamond-shaped line of Dirac nodes. We also show that the square Si lattice in ZrSiS is an excellent template for realizing new types of two-dimensional Dirac cones recently predicted by Young and Kane. Finally, we find that the energy range of the linearly dispersed bands is as high as 2 eV above and below the Fermi level; much larger than of other known Dirac materials. This makes ZrSiS a very promising candidate to study Dirac electrons, as well as the properties of lines of Dirac nodes.

Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations

“…2a). Such 2D characteristics are reminiscent of the surface state observed in the ARPES experiments, which is hybridized with the non-symmorphic symmetry-protected Dirac state [45]. However,…”

“…1c) and overall 3D nature, the F α -band probed in our dHvA experiments should be from a bulk state, rather than surface states. Given the nearly zero effective mass and ultra-high quantum mobility (Table 1), one might ascribe the F α band to the non-symmorphic 2D Dirac band in ZrSiS, which are expected to display superior Dirac fermion properties due to gapless Dirac crossings protected by the non-symmorphic symmetry [45,49]. However, though ZrSiS has been known as be the first material hosting such a non-symmorphic Dirac state [45], the non-symmorphic Dirac node is ~ 0.5 eV below the Fermi level, and thus is not expected to generate observable effects in quantum oscillations.…”

“…Among these materials, ZrSiS, which possesses layered tetragonal structure (see Fig. 1a) [43,45,48], shows distinct properties.…”

“…In addition to the aforementioned topological semimetals with discrete Dirac/Weyl nodes, a new type of topological semimetal with Dirac bands crossing along a one-dimensional line in momentum space has also been predicted [35][36][37][38][39][40][41][42][43] and experimentally observed in several compounds such as PbTaSe 2 [44], ZrSiS [45][46], and PtSn 4 [47]. Among these materials, ZrSiS, which possesses layered tetragonal structure (see Fig.…”

“…Firstly, the energy bands crossing the Fermi level in ZrSiS are all Dirac bands [45], making it an be well fitted to the LK model [55], since the oscillating magnetization directly originates from the oscillations of electrons' free energy. As a result, the dHvA effects can provide more direct information on Fermi surface (FS), particularly for those materials that are not exactly three dimensional (3D), such as ZrSiS which possesses a layered structure (Fig.…”