Ma J-Z, Wu Q-S, Song M, Zhang S-N, Guedes E B, Ekahana S A, Krivenkov M, Yao M Y, Gao S-Y, Fan W-H, Qian T, Ding H, Plumb N C, Radovic M, Dil J H, Xiong Y-M, Manna K, Felser C, Yazyev O V, Shi M
Photon Science Division, Paul Scherrer Institute, Villigen PSI, Switzerland.
Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, China.
Nat Commun. 2021 Jun 28;12(1):3994. doi: 10.1038/s41467-021-24289-0.
Constrained by the Nielsen-Ninomiya no-go theorem, in all so-far experimentally determined Weyl semimetals (WSMs) the Weyl points (WPs) always appear in pairs in the momentum space with no exception. As a consequence, Fermi arcs occur on surfaces which connect the projections of the WPs with opposite chiral charges. However, this situation can be circumvented in the case of unpaired WP, without relevant surface Fermi arc connecting its surface projection, appearing singularly, while its Berry curvature field is absorbed by nontrivial charged nodal walls. Here, combining angle-resolved photoemission spectroscopy with density functional theory calculations, we show experimentally that a singular Weyl point emerges in PtGa at the center of the Brillouin zone (BZ), which is surrounded by closed Weyl nodal walls located at the BZ boundaries and there is no Fermi arc connecting its surface projection. Our results reveal that nontrivial band crossings of different dimensionalities can emerge concomitantly in condensed matter, while their coexistence ensures the net topological charge of different dimensional topological objects to be zero. Our observation extends the applicable range of the original Nielsen-Ninomiya no-go theorem which was derived from zero dimensional paired WPs with opposite chirality.
受尼尔森 - 二宫禁则定理的限制，在所有迄今为止通过实验确定的外尔半金属（WSMs）中，外尔点（WPs）在动量空间中总是成对出现，无一例外。因此，费米弧出现在连接具有相反手征电荷的WPs投影的表面上。然而，在未配对的WP情况下，这种情况可以被规避，其表面投影没有相关的表面费米弧连接，单独出现，而其贝里曲率场被非平凡带电节点壁吸收。在这里，结合角分辨光电子能谱和密度泛函理论计算，我们通过实验表明，在布里渊区（BZ）中心的PtGa中出现了一个奇异外尔点，它被位于BZ边界的封闭外尔节点壁包围，并且没有费米弧连接其表面投影。我们的结果表明，不同维度的非平凡能带交叉可以在凝聚态物质中同时出现，而它们的共存确保了不同维度拓扑对象的净拓扑电荷为零。我们的观察扩展了原始尼尔森 - 二宫禁则定理的适用范围，该定理是从具有相反手征性的零维配对WPs推导出来的。
