Topological Phases without Crystalline Counterparts

Dániel Varjas, Alexander Lau, Kim Pöyhönen, Anton R. Akhmerov, Dmitry I. Pikulin, and Ion Cosma Fulga
Phys. Rev. Lett. 123, 196401 – Published 7 November 2019
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Abstract

We construct a two-dimensional higher-order topological phase protected by a quasicrystalline eightfold rotation symmetry. Our tight-binding model describes a superconductor on the Ammann-Beenker tiling hosting localized Majorana zero modes at the corners of an octagonal sample. In order to analyze this model, we introduce Hamiltonians generated by a local rule, and use this concept to identify the bulk topological properties. We find a Z2 bulk topological invariant protecting the corner modes. Our work establishes that there exist topological phases protected by symmetries impossible in a crystal.

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  • Received 17 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.196401

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Dániel Varjas1,2,*, Alexander Lau2, Kim Pöyhönen1,2, Anton R. Akhmerov2, Dmitry I. Pikulin3, and Ion Cosma Fulga4

  • 1QuTech, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
  • 2Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands
  • 3Microsoft Quantum, Microsoft Station Q, University of California, Santa Barbara, California 93106-6105, USA
  • 4IFW Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtzstrasse 20, 01069 Dresden, Germany

  • *dvarjas@gmail.com

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Issue

Vol. 123, Iss. 19 — 8 November 2019

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