Dirac node lines in two-dimensional Lieb lattices.

As a new type of quantum matter, Dirac node line (DNL) semimetals are currently attracting widespread interest in condensed matter physics and materials science. The DNL, featured by a closed line consisting of linear band crossings in the momentum space, was mostly predicted in three-dimensional materials. Here, we propose a tight-binding (TB) model of p + p or p + s orbitals defined on the two-dimensional (2D) Lieb lattice for the 2D version of DNL semimetals. The DNL states in these models are caused by the inversion of the bands with different symmetries and thus robust against spin-orbit interaction. By means of first-principles calculations, we demonstrate two candidate materials: BeC and BeH monolayers, which have Fermi circles centred at Γ(0,0) and K(1/2,1/2) points, respectively. Their Fermi velocities are higher than that in graphene. The non-zero Z topological invariant accompanied by the edge states is revealed in these materials. This work opens an avenue for the design of 2D DNL semimetals.