Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice

Abstract

Non-symmorphic symmetries protect Dirac nodal lines and cones in lattice systems. Here, we investigate the spectral properties of a two-dimensional lattice belonging to a non-symmorphic group. Specifically, we look at the herringbone lattice, characterised by two sets of glide symmetries applied in two orthogonal directions. We describe the system using a nearest-neighbour tight-binding model containing horizontal and vertical hopping terms. We find two non-equivalent Dirac cones inside the first Brillouin zone along a high-symmetry path. We tune these Dirac cones' positions by breaking the lattice symmetries using onsite potentials. These Dirac cones can merge into a semi-Dirac cone or unfold along a high-symmetry path. Finally, we perturb the system by applying a dimerization of the hopping terms. We report a flow of Dirac cones inside the first Brillouin zone describing quasi-hyperbolic curves. We present an implementation in terms of CO atoms placed on the top of a Cu(111) surface.

12 pages with 9 figures and supplemental material; in press

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• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Tight-binding model with sublattice-asymmetric spin-orbit coupling for square-net nodal line Dirac semimetals
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets
• Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems