Fig. 3: The electronic band structures of Lieb lattices.

a, b Schematic diagram of the band structures and the proportion of NM metal (NM-M), Dirac semimetal (DSM), FM half metal (FM-HM), and AFM semiconductor (AFM-SC). c Band structures of Be2C, Ag2N, WO2, RuO2, and TiF2. Dirac points, type-II Dirac points, van Hove singularities, and flat bands are marked by brown, green, red, and cyan dashed lines, respectively. d, e Three-dimensional band structures showing nodal-loop of Be2C and flat bands of TiF2.