Topological Phases without Crystalline Counterparts

Dániel Varjas, Alexander Lau, Kim Pöyhönen, Anton R. Akhmerov, Dmitry I. Pikulin, Ion Cosma Fulga

Research output: Contribution to journalArticleScientificpeer-review

83 Citations (Scopus)
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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.

Original languageEnglish
Article number196401
Number of pages6
JournalPhysical Review Letters
Issue number19
Publication statusPublished - 2019


  • exotic phases of matter
  • majorana bound states
  • symmetry protected topological states
  • topological materials


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