Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

TL;DR

This paper investigates the topological surface states in ZrSiTe, revealing how a $ ext{Z}_2$ Berry phase structure leads to a modular arithmetic of surface states, confirmed by experiments and calculations.

Contribution

It provides the first comprehensive characterization of topological surface states in square-net nodal line semimetals, linking Berry phase topology to surface state behavior.

Findings

Identification of topological drumhead surface states in ZrSiTe

Demonstration of $ ext{Z}_2$ modular arithmetic governing surface state hybridization

Experimental and theoretical confirmation of surface state topology

Abstract

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. Using the spectra of Wilson loops, we show that a non-trivial Berry phase that exists 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 \textit{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.