• Open Access

Modular Arithmetic with Nodal Lines: Drumhead Surface States in ZrSiTe

Lukas Muechler, Andreas Topp, Raquel Queiroz, Maxim Krivenkov, Andrei Varykhalov, Jennifer Cano, Christian R. Ast, and Leslie M. Schoop
Phys. Rev. X 10, 011026 – Published 6 February 2020

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, which can be easily distinguished in ARPES experiments. Using the spectra of Wilson loops, we show that a nontrivial Berry phase that exists 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 derived 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 work is the first complete characterization of topological surface states in the family of square-net-based nodal line semimetals, and thus it fundamentally increases the understanding of the topological nature of this growing class of topological semimetals.

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  • Received 14 August 2019
  • Revised 18 November 2019
  • Accepted 16 December 2019

DOI:https://doi.org/10.1103/PhysRevX.10.011026

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Lukas Muechler1,*, Andreas Topp2, Raquel Queiroz3, Maxim Krivenkov4, Andrei Varykhalov4, Jennifer Cano1,5, Christian R. Ast2, and Leslie M. Schoop6,†

  • 1Center for Computational Quantum Physics, The Flatiron Institute, New York, New York, 10010, USA
  • 2Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
  • 3Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel
  • 4Helmholtz-Zentrum Berlin für Materialien und Energie, Elektronenspeicherring BESSY II, Albert-Einstein-Straße 15, 12489 Berlin, Germany
  • 5Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
  • 6Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

  • *lmuechler@flatironinstitute.org
  • lschoop@princeton.edu

Popular Summary

Nodal semimetals are metals in which the valence and conduction bands connect to form lines or loops, so-called nodal lines. They have long been studied for their unusual electronic and optical properties. One example is the appearance of topologically protected “drumhead surface states,” surface states that originate from band touching points in the bulk material. However, these states have remained elusive in one of the most heavily studied families of nodal semimetals. Here, we experimentally show for the first time that drumhead surface states can be found in one member of this family.

To look for drumhead surface states, we study the electronic structure of the nodal semimetal ZrSiTe, which possesses multiple nodal lines and therefore multiple drumhead surface states. Through ab initio calculations and angle-resolved photoemission experiments, we unravel the resulting complex surface states of this material and show how the different drumhead states interact with each other. We find that the electronic structure of the surface can be understood from the bulk electronic structure, in particular, the relative arrangement of the nodal lines.

Our study completes the topological classification of materials in the ZrSiS family and opens an avenue to further study the interplay of symmetry, topology, and surface states in complex materials.

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Vol. 10, Iss. 1 — January - March 2020

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