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.

BaAl ₄原型晶体结构是所有结构类型中人口最多的，并且是各种子结构集的基础，包括著名的ThCr ₂ Si ₂族，该族具有高温超导性以及众多磁性和强相关电子系统。MA ₄族材料（M = Sr，Ba，Eu； A = Al，Ga，In）本身呈现出一组有趣的基态，包括电荷和自旋序，但在很大程度上被认为是无趣的金属。我们预测示例性化合物BaAl ₄包含具有非平凡拓扑的三维Dirac频谱和可能的节点线穿过布里渊区，其中存在一对在k _z方向上具有线性色散且在k _x / k _y方向上具有二次色散的半Dirac点在旋转轴上具有C _{4 v}点群对称性。BaAl _4中的超大不饱和正磁电阻尽管揭示了未补偿的能带结构，并且量子振荡和角度分辨光发射光谱法测量结果证实了预测的多带半金属结构，并具有Dirac空穴和Van Hove奇异性（VHS），与理论预测非常一致。因此，我们将BaAl ₄视为一种拓扑半金属，将其原型状态转变为各种拓扑材料的基础。