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As a new type of quantum matter, Dirac node line (DNL) semimetals arecurrently attracting widespread interest in condensed matter physics andmaterial science. The DNL featured by a closed line consisting of linear bandcrossings in the lattice momentum space are mostly predicted inthree-dimensional materials. Here, we propose tight-binding (TB) models ofpz/px,y or pz/s orbitals in a two-dimensional (2D) bipartite square lattice forthe 2D version of DNL semimetals. The DNL states in these models are caused bythe inversion of the bands with different symmetries and thus robust againspin-orbit coupling (SOC). By means of first-principles calculations, wedemonstrate two candidate 2D materials of these models: Be2C and BeH2monolayers, which have Fermi circles centered at {\Gamma} (0,0) and K (1/2,1/2) points, respectively. The topological nontriviality is verified by thenon-zero topological invariant and the edge states. This work opens an avenuefor design of 2D DNL semimetals.

Dirac node lines in a two-dimensional bipartite square lattice