Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
We study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions with certain on-site symmetries. They are crystalline SPT phases, which are distinguished from a trivial product state only in the presence of non-symmorphic glide symmetry. We classify...
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| Format: | Article |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
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| Online Access: | https://doi.org/10.1088/1367-2630/aa769b |
| _version_ | 1827873318045220864 |
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| author | Fuyan Lu Bowen Shi Yuan-Ming Lu |
| author_facet | Fuyan Lu Bowen Shi Yuan-Ming Lu |
| author_sort | Fuyan Lu |
| collection | DOAJ |
| description | We study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions with certain on-site symmetries. They are crystalline SPT phases, which are distinguished from a trivial product state only in the presence of non-symmorphic glide symmetry. We classify these GSPT phases with various on-site symmetries such as U (1) and time reversal, and show that they can all be understood by stacking and coupling two-dimensional (2D) short-range-entangled phases in a glide-invariant way. Using such a coupled layer construction we study the anomalous surface topological orders of these GSPT phases, which gap out the 2D surface states without breaking any symmetries. While this framework can be applied to any non-symmorphic SPT phase, we demonstrate it in many examples of GSPT phases including the non-symmorphic topological insulator with ‘hourglass fermion’ surface states. |
| first_indexed | 2024-03-12T16:35:30Z |
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| id | doaj.art-645fe08233204c3081baaad0071d0fe9 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:30Z |
| publishDate | 2017-01-01 |
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| spelling | doaj.art-645fe08233204c3081baaad0071d0fe92023-08-08T14:53:38ZengIOP PublishingNew Journal of Physics1367-26302017-01-0119707300210.1088/1367-2630/aa769bClassification and surface anomaly of glide symmetry protected topological phases in three dimensionsFuyan Lu0Bowen Shi1Yuan-Ming Lu2Department of Physics, The Ohio State University , Columbus, OH 43210, United States of AmericaDepartment of Physics, The Ohio State University , Columbus, OH 43210, United States of AmericaDepartment of Physics, The Ohio State University , Columbus, OH 43210, United States of AmericaWe study glide protected topological (GSPT) phases of interacting bosons and fermions in three spatial dimensions with certain on-site symmetries. They are crystalline SPT phases, which are distinguished from a trivial product state only in the presence of non-symmorphic glide symmetry. We classify these GSPT phases with various on-site symmetries such as U (1) and time reversal, and show that they can all be understood by stacking and coupling two-dimensional (2D) short-range-entangled phases in a glide-invariant way. Using such a coupled layer construction we study the anomalous surface topological orders of these GSPT phases, which gap out the 2D surface states without breaking any symmetries. While this framework can be applied to any non-symmorphic SPT phase, we demonstrate it in many examples of GSPT phases including the non-symmorphic topological insulator with ‘hourglass fermion’ surface states.https://doi.org/10.1088/1367-2630/aa769bsymmetry protected topological phasenon-symmorphic symmetrytopological order |
| spellingShingle | Fuyan Lu Bowen Shi Yuan-Ming Lu Classification and surface anomaly of glide symmetry protected topological phases in three dimensions New Journal of Physics symmetry protected topological phase non-symmorphic symmetry topological order |
| title | Classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| title_full | Classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| title_fullStr | Classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| title_full_unstemmed | Classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| title_short | Classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| title_sort | classification and surface anomaly of glide symmetry protected topological phases in three dimensions |
| topic | symmetry protected topological phase non-symmorphic symmetry topological order |
| url | https://doi.org/10.1088/1367-2630/aa769b |
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