Two-Dimensional Node-Line Semimetals in a Honeycomb-Kagome Lattice^*

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 (NLSs). In particular, several compounds (e.g., certain 3D graphene networks, Cu ${}_3$ PdN, Ca ${}_3$ P ${}_2$ ) were discovered to be 3D NLSs, in which the conduction and valence bands cross at closed lines in the Brillouin zone. Except for the two-dimensional (2D) Dirac semimetal (e.g., graphene), 2D topological semimetals are much less investigated. Here we propose a new concept of a 2D NLS and suggest that this state could be realized in a new mixed lattice (named as HK lattice) composed by Kagome and honeycomb lattices. It is found that A ${}_3$ B ${}_2$ (A is a group-IIB cation and B is a group-VA anion) compounds (such as Hg ${}_3$ As ${}_2$ ) with the HK lattice are 2D NLSs due to the band inversion between the cation Hg-s orbital and the anion As- $p_z$ orbital with respect to the mirror symmetry. Since the band inversion occurs between two bands with the same parity, this peculiar 2D NLS could be used as transparent conductors. In the presence of buckling or spin-orbit coupling, the 2D NLS state may turn into a 2D Dirac semimetal state or a 2D topological crystalline insulating state. Since the band gap opening due to buckling or spin-orbit coupling is small, Hg ${}_3$ As ${}_2$ with the HK lattice can still be regarded as a 2D NLS at room temperature. Our work suggests a new route to design topological materials without involving states with opposite parities. (express letter)