%0 Journal Article %1 PhysRevLett.123.196401 %A Varjas, Dániel %A Lau, Alexander %A Pöyhönen, Kim %A Akhmerov, Anton R. %A Pikulin, Dmitry I. %A Fulga, Ion Cosma %D 2019 %I American Physical Society %J Phys. Rev. Lett. %K a %N 19 %P 196401 %R 10.1103/PhysRevLett.123.196401 %T Topological phases without crystalline counterparts %U https://link.aps.org/doi/10.1103/PhysRevLett.123.196401 %V 123 %X 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.

@article{PhysRevLett.123.196401, 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.}, added-at = {2020-03-23T11:36:24.000+0100}, author = {Varjas, D\'aniel and Lau, Alexander and P\"oyh\"onen, Kim and Akhmerov, Anton R. and Pikulin, Dmitry I. and Fulga, Ion Cosma}, biburl = {https://www.bibsonomy.org/bibtex/2f405b9e14d209aaf16d482522951eae1/ctqmat}, day = 7, description = {Phys. Rev. Lett. 123, 196401 (2019) - Topological Phases without Crystalline Counterparts}, doi = {10.1103/PhysRevLett.123.196401}, interhash = {1b0017c8fc727aa0509b7150489747b0}, intrahash = {f405b9e14d209aaf16d482522951eae1}, journal = {Phys. Rev. Lett.}, keywords = {a}, month = {11}, number = 19, numpages = {6}, pages = 196401, publisher = {American Physical Society}, timestamp = {2023-10-13T12:34:57.000+0200}, title = {Topological phases without crystalline counterparts}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.123.196401}, volume = 123, year = 2019 }