By measuring the de Hass-van Alphen effect and calculating the electronic band structure, we have investigated the bulk Fermi surface of the BaSn3 superconductor with a transition temperature of ~ 4.4 K. Striking de Haas-van Alphen (dHvA) quantum oscillations are observed when the magnetic field B is perpendicular to both (100) and (001) planes. Our analysis unveiled nontrivial Berry phase imposed in the quantum oscillations when B is perpendicular to (100), with two fundamental frequencies at 31.5 T and 306.7 T, which likely arise from two corresponding hole pockets of the bands forming a type-II Dirac point. The results are supported by the ab initio calculations indicating a type-II Dirac point setting and tilting along the high symmetric K-H line of the Brillouin zone, about 0.13 eV above the Fermi level. Moreover, the calculations also revealed other two type-I Dirac points on the high symmetric {\Gamma}-A direction, but slightly far below the Fermi level. The results demonstrate BaSn3 as an excellent platform for the study of not only exotic properties of different types of Dirac fermions in a single material, but also the interplay between nontrivial topological states and superconductivity.

中文翻译：

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具有多重狄拉克费米子的 BaSn3 超导体中的 de Haas-van Alphen 量子振荡

通过测量 de Hass-van Alphen 效应并计算电子能带结构，我们研究了转变温度为 ~ 4.4 K 的 BaSn3 超导体的体费米表面。磁场 B 垂直于 (100) 和 (001) 平面。我们的分析揭示了当 B 垂直于 (100) 时，量子振荡中强加的非平凡 Berry 相位，具有 31.5 T 和 306.7 T 的两个基本频率，这可能来自形成 II 型狄拉克点的带的两个相应孔袋。结果得到了从头计算的支持，表明 II 型狄拉克点设置和沿布里渊区的高对称 KH 线倾斜，比费米能级高约 0.13 eV。而且，计算还揭示了高对称 {\Gamma}-A 方向上的其他两个 I 型狄拉克点，但略低于费米能级。结果表明，BaSn3 不仅是研究单一材料中不同类型狄拉克费米子的奇异性质，而且是研究非平凡拓扑态与超导性之间相互作用的绝佳平台。