Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

We study the electronic structure of the nodal line semimetal ZrSiTe 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 Z₂ structure of the Berry phase induces a Z₂ '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.