Unique Schrodinger semimetal state in ternary Be2P3N honeycomb lattice

Two-dimensional (2D) materials with zero band gaps are of great significance in fundamental science and potential applications but are rather scarce. Here we report a novel 2D semimetal, a ternary beryllium-phosphorus-nitrogen Be2P3N honeycomb-lattice monolayer by first-principles calculations. This graphene-like Be2P3N monolayer is composed of Be and N tricoordinated with P-3 and exhibits excellent dynamic and thermal stabilities. Unlike the semimetal graphene with linear Dirac-cone energy-momentum dispersion, the Be2P3N monolayer is intrinsically gapless with parabolic E-+/-(k) approximate to +/- k(2) band dispersion (the +/- sign corresponds to the conduction and valence bands) in the low-energy vicinity, and features a peculiar Schrodinger paraboloid. The +/- k(2) band state mainly originates from P-p(z) electrons and has high stability against large external strains. This finding opens a new branch of semimetal nanomaterials research.