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

TL;DR

This paper explores the spectral properties of a two-dimensional non-symmorphic lattice, demonstrating how Dirac cones can be tuned, merged, or unfolded through symmetry breaking and dimerization, with potential realization on a copper surface.

Contribution

It introduces a detailed analysis of Dirac cone manipulation in a non-symmorphic lattice, including symmetry breaking and dimerization effects, with an experimental implementation proposal.

Findings

Identification of two non-equivalent Dirac cones in the lattice.

Tuning of Dirac cones' positions via onsite potential symmetry breaking.

Observation of Dirac cone merging and flow under perturbations.

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.