  Recently, the concept of topological insulators has been generalized to
topological semimetals, including three-dimensional (3D) Weyl semimetals, 3D
Dirac semimetals, and 3D node-line semimetals. In particular, several compounds
(e.g., certain three-dimensional graphene networks, Cu3PdN, Ca3P2) were
discovered to be 3D node-line semimetals, in which the conduction and the
valence bands cross at closed lines in the Brillouin zone. Except for the
two-dimensional (2D) Dirac semimetal (e.g., in graphene), 2D topological
semimetals are much less investigated. Here, we propose the new concept of a 2D
node-line semimetal and suggest that this state could be realized in a new
mixed lattice (we name it as HK lattice) composed by kagome and honeycomb
lattices. We find that A3B2 (A is a group-IIB cation and B is a group-VA anion)
compounds (such as Hg3As2) with the HK lattice are 2D node-line semimetals due
to the band inversion between cation s orbital and anion pz orbital. In the
presence of buckling or spin-orbit coupling, the 2D node-line semimetal state
may turn into 2D Dirac semimetal state or 2D topological crystalline insulating
state.
