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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Topological Phases without Crystalline Counterparts.

Dániel Varjas1,2, Alexander Lau2, Kim Pöyhönen1,2

  • 1QuTech, Delft University of Technology, P.O. Box 4056, 2600 GA Delft, Netherlands.

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|November 26, 2019
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Summary

We discovered a new type of topological phase protected by quasicrystalline symmetry, hosting Majorana zero modes at the corners of octagonal samples. This reveals topological phases beyond crystalline systems.

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Area of Science:

  • Condensed Matter Physics
  • Topological Matter
  • Quasicrystalline Physics

Background:

  • Higher-order topological phases exhibit unique properties localized at boundaries of lower dimensionality.
  • Quasicrystalline symmetries, unlike periodic crystal symmetries, offer novel platforms for topological phenomena.
  • Topological superconductors host exotic excitations like Majorana zero modes.

Purpose of the Study:

  • To construct and analyze a two-dimensional higher-order topological phase protected by quasicrystalline eightfold rotation symmetry.
  • To investigate the existence and properties of Majorana zero modes in such a system.
  • To identify the bulk topological invariant protecting these localized modes.

Main Methods:

  • Development of a tight-binding model for a superconductor on an Ammann-Beenker tiling.
  • Introduction of Hamiltonians generated by a local rule for analyzing bulk topological properties.
  • Identification of a Z_{2} bulk topological invariant.

Main Results:

  • Localized Majorana zero modes were found at the corners of an octagonal sample.
  • A Z_{2} bulk topological invariant was identified, confirming the protection of corner modes.
  • The study demonstrates topological phases protected by non-crystalline symmetries.

Conclusions:

  • A novel higher-order topological phase protected by quasicrystalline symmetry has been realized.
  • The findings confirm the existence of Majorana zero modes in this system.
  • This work expands the understanding of topological phases beyond conventional crystalline systems.