Topological Band Theory for Non-Hermitian Hamiltonians
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify “gapped” bands in one and two dimensions by explicitly finding their...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114634 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-8803-1017 |
| _version_ | 1811070121013149696 |
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| author | Shen, Huitao Zhen, Bo Fu, Liang |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Shen, Huitao Zhen, Bo Fu, Liang |
| author_sort | Shen, Huitao |
| collection | MIT |
| description | We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify “gapped” bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated “exceptional points” in momentum space. We also systematically classify all types of band degeneracies. |
| first_indexed | 2024-09-23T08:25:48Z |
| format | Article |
| id | mit-1721.1/114634 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:25:48Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1146342022-09-30T09:18:00Z Topological Band Theory for Non-Hermitian Hamiltonians Shen, Huitao Zhen, Bo Fu, Liang Massachusetts Institute of Technology. Department of Physics Shen, Huitao Zhen, Bo Fu, Liang We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify “gapped” bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated “exceptional points” in momentum space. We also systematically classify all types of band degeneracies. United States. Department of Energy. Office of Basic Energy Sciences (Award DE-SC0010526) Massachusetts Institute of Technology. Institute for Soldier Nanotechnologies (Contract W911NF-13-D-0001) United States. Air Force Office of Scientific Research (Grant FA9550-18-1-0133) 2018-04-09T18:00:29Z 2018-04-09T18:00:29Z 2018-04 2017-08 2018-04-06T18:00:15Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/114634 Shen, Huitao et al. "Topological Band Theory for Non-Hermitian Hamiltonians." Physical Review Letters 120, 14 (April 2018): 146402 © 2018 American Physical Society https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-8803-1017 en http://dx.doi.org/10.1103/PhysRevLett.120.146402 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Shen, Huitao Zhen, Bo Fu, Liang Topological Band Theory for Non-Hermitian Hamiltonians |
| title | Topological Band Theory for Non-Hermitian Hamiltonians |
| title_full | Topological Band Theory for Non-Hermitian Hamiltonians |
| title_fullStr | Topological Band Theory for Non-Hermitian Hamiltonians |
| title_full_unstemmed | Topological Band Theory for Non-Hermitian Hamiltonians |
| title_short | Topological Band Theory for Non-Hermitian Hamiltonians |
| title_sort | topological band theory for non hermitian hamiltonians |
| url | http://hdl.handle.net/1721.1/114634 https://orcid.org/0000-0002-7572-4594 https://orcid.org/0000-0002-8803-1017 |
| work_keys_str_mv | AT shenhuitao topologicalbandtheoryfornonhermitianhamiltonians AT zhenbo topologicalbandtheoryfornonhermitianhamiltonians AT fuliang topologicalbandtheoryfornonhermitianhamiltonians |