The Interplay of Topology and Symmetry in Non-Symmorphic Square-Net Tellurides Probed by Scanning Tunnelling Microscopy

The non-symmorphic square-net materials have been of interest due to their symmetry enforced band crossings giving rise to Dirac nodal loops and both topologically trivial and non-trivial surface states. Crystals of the P4/nmm space group feature a plane of atoms in a square net (e.g. the Si plane in the ZrSiX family or Sn plane in RESnX family) with a 2-atom unit cell due to the surrounding lattice. This doubling of the square net unit cell, along with glide plane symmetry enforces a degeneracy at the edge of the Brillouin zone driving a crossing of different orbital symmetry that prevent hybridization. These features give rise to wide-bandwidth linear crossings which revolve around the Brillouin zone enclosing regions of distinct topology.<br/><br/>I will describe our recent work on two of these materials: ZrSiTe which exhibits a topologically non-trivial surface state, and LaSbTe which has a doping-dependent structural distortion that gaps portions of the nodal loop. Using Scanning Tunnelling Microscopy and Spectroscopy (STM/STS), we have investigated the surface structure and electronic states through quasiparticle interference (QPI) measurements. In ZrSiTe, the large area between two nodal loops hosts a topologically non-trivial “drumhead” surface state, previously observed up to Ef by ARPES¹. However, the presence of spin-orbit coupling in this system gaps the nodal lines, raising the question of what happens to the drumhead state. Using QPI we observed strong signatures of the drumhead state below and above E_f confirming this topologically protected state persists, owing to the small energy scale of spin-orbit coupling relative to the large band width of the nodal lines². We find that the drumhead state disperses over an energy range of ~600meV and is split, but not gapped by the presence of spin-orbit coupling.<br/><br/>Unlike the mild perturbation of spin-orbit coupling, changes in symmetry (perhaps obviously) break the symmetry-enforced protection of the nodal-lines giving the potential for much larger gap openings. While Si square net is held together by strong interaction with Zr, the square nets with rare-earths off plane are prone to distortion from the heavily nested Fermi surface. Indeed, stoichiometric LaSbTe forms in an orthorhombic phase featuring a buckled square-net with zig-zag chains, with a gap opening in the nodal-lines in Γ-S direction. Here we have investigated the surface structure and electronic states of twinned <i>o</i>-LaSbTe. The zig-zag rows of the Sb lattice can be seen in STM images, and a soft-gap of ~300meV can be observed consistent with DFT calculations for the distorted structure. Twin-boundaries show the two perpendicular orientations with domain “walls” several unit cells wide that appear tetragonal. Highly directional QPI is seen around Sb-lattice defect sites and is consistent with scattering from the remaining pockets of the nodal loops appearing in the tetragonal phase. I will also discuss the potential for doping to traverse this phase diagram and topological implications of these structural changes.<br/><br/>1 L. Müchler, et al. PRX 10, 011026 (2020)<br/>2 B. Stuart, et al. PRB 105, L121111 (2022)