Crystalline symmetry-protected non-trivial topology in prototype compound BaAl₄

The BaAl₄ prototype crystal structure is the most populous of all structure types, and is the building block for a diverse set of sub-structures including the famous ThCr₂Si₂ family that hosts high-temperature superconductivity and numerous magnetic and strongly correlated electron systems. The MA₄ family of materials (M = Sr, Ba, Eu; A = Al, Ga, In) themselves present an intriguing set of ground states including charge and spin orders, but have largely been considered as uninteresting metals. We predict the exemplary compound BaAl₄ to harbor a three-dimensional Dirac spectrum with non-trivial topology and possible nodal lines crossing the Brillouin zone, wherein one pair of semi-Dirac points with linear dispersion along the k_z direction and quadratic dispersion along the k_x/k_y direction resides on the rotational axis with C_4v point group symmetry. An extremely large, unsaturating positive magnetoresistance in BaAl₄ despite an uncompensated band structure is revealed, and quantum oscillations and angle-resolved photoemission spectroscopy measurements confirm the predicted multiband semimetal structure with pockets of Dirac holes and a Van Hove singularity (VHS) remarkably consistent with the theoretical prediction. We thus present BaAl₄ as a topological semimetal, casting its prototype status into a role as a building block for a vast array of topological materials.