ZrSiS was shown in 2016 (Schoop et al., Nat. Commun. 7, 11696) to host a diamond-shaped line of Dirac nodes, a two-dimensional Dirac cone at the Brillouin-zone X point protected by non-symmorphic symmetry and lying about 0.5 eV0.5\,\mathrm{eV} below the Fermi level, and an unconventional surface-derived state hybridizing with the bulk Dirac bands around X. The paper posed three follow-up objectives: explain the hybridizing surface state, tune the Fermi energy into the X-point crossing so the non-symmorphic 2D Dirac fermions predicted by Young and Kane could be studied directly, and measure the magnetotransport implied by the Dirac line node. Later literature has resolved the first objective and the bulk-transport part of the third: the surface state is a 'floating' two-dimensional band generated by surface symmetry breaking, and ZrSiS exhibits extremely large, anisotropic, non-saturating magnetoresistance. The surviving open core is whether the Fermi energy of ZrSiS itself can be shifted by roughly 0.5 eV0.5\,\mathrm{eV} through hole doping or gating so that the X-point 2D Dirac fermions become experimentally accessible, and whether the topological drumhead surface states of ZrSiS can be cleanly isolated from the trivial bulk and surface bands that dominate its quasiparticle interference.

Background

ZrSiS is a layered, air-stable, earth-abundant compound (PbFCl structure type, tetragonal space group P4/nmmP4/nmm) built from square nets of Si sandwiched between Zr and S layers. In band-structure terms it is a topological nodal-line semimetal: instead of isolated Dirac points, its valence and conduction bands cross along closed loops in momentum space, here a diamond-shaped loop around the Brillouin-zone center that produces a diamond-shaped Fermi surface. Nodal-line semimetals are predicted to host 'drumhead' surface states — nearly flat, strongly two-dimensional surface bands bound to the area of the surface Brillouin zone enclosed by the projected nodal loop — in contrast to the Fermi-arc surface states of Weyl semimetals (semimetals whose isolated, linear, topologically protected band crossings project onto open surface arcs connecting them). A symmetry is called non-symmorphic when it combines a rotation or reflection with a fractional lattice translation (ZrSiS contains glide planes); at Brillouin-zone boundary points such as X, such symmetries force bands of different character to be degenerate, so that Dirac crossings there survive even strong spin–orbit coupling. Young and Kane predicted that two-dimensional lattices with these symmetries host a new class of 2D Dirac cones that cannot be gapped by spin–orbit coupling, with 2D Dirac fermions distinct from those of graphene. Angle-resolved photoemission spectroscopy (ARPES) — which maps band dispersions on the cleaved crystal surface — showed that ZrSiS realizes this template: its Si square net produces a non-symmorphically protected Dirac cone at the X point, seen in ARPES at about −0.5 eV-0.5\,\mathrm{eV}, with linearly dispersing bands extending roughly 2 eV2\,\mathrm{eV} in energy. Because the crossing lies far below the native Fermi level (with other bands present at that energy), the paper proposed that hole doping on the Zr or S site, or electrostatic gating of thin films (shifting the Fermi energy with a gate electrode; in thin flakes, ionic-liquid gating, where an electrolyte's ions form a nanometer-scale capacitor at the surface, reaches the largest carrier-density changes) might bring the Fermi energy into the crossing and open the 2D Dirac fermions to direct transport and spectroscopic study. The same ARPES data revealed a surface-derived state that penetrates the projected bulk bands and hybridizes with the bulk cone at X — behavior the authors flagged as uncommon and requiring further investigation — and the authors anticipated high carrier mobility and large magnetoresistance from the line-node bands. Subsequent work clarified the surface state (a 'floating' 2D band created when the reduced symmetry at the cleavage plane lifts the degeneracies imposed by non-symmorphic bulk symmetries) and measured the magnetotransport (extremely large, anisotropic, non-saturating magnetoresistance), but the Fermi level of ZrSiS has not been demonstrated to reach the X-point crossing, and in quasiparticle-interference experiments — which image, by scanning tunneling microscopy, the standing-wave patterns that quasiparticles scattered from defects imprint on the surface density of states — the drumhead surface states of ZrSiS itself remain masked by trivial bulk and floating surface bands.

Problem Statement

The 2016 discovery paper for ZrSiS posed three linked follow-up objectives, of which two have since been substantially addressed by the literature (the origin of the hybridizing surface state as a floating 2D band, and the bulk magnetotransport). The surviving open problem is the remaining experimental program needed to make the non-symmorphic and line-node band features of ZrSiS directly accessible: (1) Can the Fermi energy of ZrSiS be tuned — by hole doping on the Zr or S site, by chemical substitution, or by electrostatic or ionic-liquid gating of thin flakes — into the non-symmorphic-symmetry-protected Dirac crossing at the Brillouin-zone X point, which lies roughly 0.5 eV0.5\,\mathrm{eV} below the Fermi level of as-grown crystals, and can this tuning be done reproducibly in the bulk (not only at a dosed surface) while preserving the nonsymmorphic degeneracy? (2) Once the Fermi level is at (or tunably across) the crossing, what are the transport and spectroscopic signatures of the two-dimensional Dirac fermions predicted by Young and Kane — for example their Landau levels, quantum oscillations, and Hall response — given that other bands coexist at that energy? (3) Can the topologically non-trivial drumhead surface states associated with the projected Dirac nodal loop be cleanly isolated in ZrSiS itself, given that quasiparticle-interference and scanning-tunneling measurements on ZrSiS and ZrSiSe are dominated by trivial bulk bands and floating surface states? A complete answer would establish whether ZrSiS, rather than only its sister compounds (e.g. ZrSiTe, where the non-symmorphic degeneracy already lies near the Fermi level), can serve as the material platform for non-symmorphic 2D Dirac fermion and line-node surface-state physics that the source paper proposed. These three sub-questions are independently refutable: (1) whether the Fermi energy can be tuned into the X-point crossing reproducibly in the bulk while preserving the nonsymmorphic degeneracy; (3) whether the drumhead states can be cleanly isolated; and (2) is conditional — it presupposes a positive answer to (1) and is moot if (1) is answered negatively — so a negative answer to (1) does not by itself settle (3).

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