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We developed a model for high-order topological insulators in quasicrystals, revealing corner modes with fractional charge protected by rotational symmetry. Majorana corner modes are also generated in superconducting quasicrystals.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Physics

Background:

  • High-order topological insulators (HOTIs) exhibit protected boundary states.
  • Existing theories for HOTIs are based on crystalline symmetries and momentum space, limiting their application to quasicrystals.
  • Quasicrystals possess unique rotational symmetries incompatible with traditional crystal momentum frameworks.

Purpose of the Study:

  • To develop a theoretical framework for high-order topological insulator states in two-dimensional quasicrystals.
  • To investigate the role of rotational symmetries in protecting topological states in quasicrystals.
  • To explore the creation of novel topological excitations, including fractional and Majorana corner modes.

Main Methods:

  • Development of a low-energy effective k·p Hamiltonian for quasicrystals.
  • Implementation of a novel Fourier transform tailored for quasicrystal structures.
  • Approximation of long-wavelength behavior using large-scale averages.
  • Numerical verification using tight-binding calculations.

Main Results:

  • A model capturing band inversion at the center of the pseudo-Brillouin zone in quasicrystals.
  • Prediction of fractional charge corner modes induced by an in-plane Zeeman field, protected by rotational symmetry.
  • Demonstration of Majorana corner modes in s-wave superconducting quasicrystals.

Conclusions:

  • The developed model provides a generic approach to studying low-energy physics in quasicrystals.
  • Rotational symmetries in quasicrystals can protect topological states and lead to exotic phenomena.
  • The findings open avenues for exploring topological excitations and fractional statistics in quasicrystalline materials.