Topological Phases without Crystalline Counterparts
Dániel Varjas (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - QRD/Kouwenhoven Lab)
Alexander Lau (TU Delft - QN/Akhmerov Group, Kavli institute of nanoscience Delft)
K.K. Pöyhönen (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - QRD/Wimmer Group)
A. R. Akhmerov (Kavli institute of nanoscience Delft, TU Delft - QN/Akhmerov Group)
Dmitry I. Pikulin (University of California)
Ion C. Fulga (IFW Dresden)
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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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