Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping
In this report, we present an analysis of a non-Hermitian extension of the Haldane model induced by non-reciprocal coupling. This study is novel as non- reciprocal couplings in the Haldane model have not received considerable attention. Prior to the introduction of this model, the concepts of band t...
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| Format: | Final Year Project (FYP) |
| Language: | English |
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Nanyang Technological University
2023
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| Online Access: | https://hdl.handle.net/10356/166577 |
| _version_ | 1824454762558390272 |
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| author | Law, Yi Khing |
| author2 | Zhang Baile |
| author_facet | Zhang Baile Law, Yi Khing |
| author_sort | Law, Yi Khing |
| collection | NTU |
| description | In this report, we present an analysis of a non-Hermitian extension of the Haldane model induced by non-reciprocal coupling. This study is novel as non- reciprocal couplings in the Haldane model have not received considerable attention. Prior to the introduction of this model, the concepts of band topology and topo- logical insulators are reviewed, with a dive into the Hermitian Haldane model as a paradigmatic example. In the Haldane model, distinct topological phases and chiral edge states associated with the nontrivial phase are studied. The complexities of the non-Hermitian regime and the new degrees of freedom it introduces in band topology are then delved into. A study on the Hatano-Nelson model is conducted to review the non-Hermitian skin effect, an elusive phenomenon that arises when non-Hermiticity is introduced. Finally, we carry out the formulation for the non- Hermitian extension of the Haldane model. The degeneracies in the non-Hermitian framework are categorized, followed by the Chern number topological phase transi- tions. In the presence of non-Hermiticity however, there is a failure of the correspon- dence between the bulk and the boundary which is attributed to the non-Hermitian skin effect. The report concludes with a depiction of the non-Hermitian skin effect in the form of a square geometry under open boundary conditions. |
| first_indexed | 2025-02-19T03:27:28Z |
| format | Final Year Project (FYP) |
| id | ntu-10356/166577 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2025-02-19T03:27:28Z |
| publishDate | 2023 |
| publisher | Nanyang Technological University |
| record_format | dspace |
| spelling | ntu-10356/1665772023-05-08T15:39:18Z Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping Law, Yi Khing Zhang Baile School of Physical and Mathematical Sciences blzhang@ntu.edu.sg Science::Physics In this report, we present an analysis of a non-Hermitian extension of the Haldane model induced by non-reciprocal coupling. This study is novel as non- reciprocal couplings in the Haldane model have not received considerable attention. Prior to the introduction of this model, the concepts of band topology and topo- logical insulators are reviewed, with a dive into the Hermitian Haldane model as a paradigmatic example. In the Haldane model, distinct topological phases and chiral edge states associated with the nontrivial phase are studied. The complexities of the non-Hermitian regime and the new degrees of freedom it introduces in band topology are then delved into. A study on the Hatano-Nelson model is conducted to review the non-Hermitian skin effect, an elusive phenomenon that arises when non-Hermiticity is introduced. Finally, we carry out the formulation for the non- Hermitian extension of the Haldane model. The degeneracies in the non-Hermitian framework are categorized, followed by the Chern number topological phase transi- tions. In the presence of non-Hermiticity however, there is a failure of the correspon- dence between the bulk and the boundary which is attributed to the non-Hermitian skin effect. The report concludes with a depiction of the non-Hermitian skin effect in the form of a square geometry under open boundary conditions. Bachelor of Science in Physics and Mathematical Sciences 2023-05-05T07:48:58Z 2023-05-05T07:48:58Z 2023 Final Year Project (FYP) Law, Y. K. (2023). Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/166577 https://hdl.handle.net/10356/166577 en application/pdf Nanyang Technological University |
| spellingShingle | Science::Physics Law, Yi Khing Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title | Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title_full | Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title_fullStr | Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title_full_unstemmed | Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title_short | Non-Hermitian extension of the Haldane model induced by non-reciprocal hopping |
| title_sort | non hermitian extension of the haldane model induced by non reciprocal hopping |
| topic | Science::Physics |
| url | https://hdl.handle.net/10356/166577 |
| work_keys_str_mv | AT lawyikhing nonhermitianextensionofthehaldanemodelinducedbynonreciprocalhopping |