We study the electronic structure of the nodal line semimetal both experimentally and theoretically. We find two different surface states in ZrSiTe - topological drumhead surface states and trivial floating band surface states, which can be easily distinguished in ARPES experiments. Using the spectra of Wilson loops, we show that a non-trivial Berry phase that exist in a confined region within the Brillouin Zone gives rise to the topological drumhead-type surface states. The ${\mathbb{Z}}_2$ structure of the Berry phase induces a ${\mathbb{Z}}_2$ ‘modular arithmetic’ of the surface states, allowing surface states deriving from different nodal lines to hybridize and gap out, which can be probed by a set of Wilson loops. Our findings are confirmed by ab-initio calculations and angle-resolved photoemission experiments, which are in excellent agreement with each other and the topological analysis. This is the first complete characterization of topological surface states in the family of square-net based nodal line semimetals and thus fundamentally increases the understanding of the topological nature of this growing class of topological semimetals.

中文翻译：

---

带有节点线的模块化算术：ZrSiTe中的鼓面表面状态

我们通过实验和理论研究节点线半金属的电子结构。我们在ZrSiTe中发现了两种不同的表面状态-拓扑鼓面表面状态和微不足道的浮动带表面状态，可以在ARPES实验中轻松地区分它们。使用威尔逊环的光谱，我们表明存在于布里渊区内有限区域中的非平凡贝里相引起了拓扑鼓面型表面状态。这${\mathbb{Z}}_{\mathrm{2个}}$ 贝里相的结构诱导 ${\mathbb{Z}}_{\mathrm{2个}}$表面状态的“模算术”，允许来自不同节点线的表面状态进行杂交和分离，可以通过一组Wilson环来探测。我们的发现得到了从头算和角度分辨的光发射实验的证实，这两者彼此之间以及与拓扑分析方面都非常吻合。这是基于平方网的节点线半金属族中拓扑表面态的第一个完整表征，因此从根本上增加了对这种增长的拓扑半金属的拓扑性质的了解。