Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands
We solve the Bogoliubov-de Gennes equations self-consistently for the d-wave order parameter in nanoscale d-wave systems with [110] surfaces and show that spontaneous time-reversal symmetry (TRS) breaking occurs at low temperatures due to a spontaneously induced complex order parameter of extended s...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/110918 |
| _version_ | 1811085005009453056 |
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| author | Nagai, Yuki Ota, Yukihiro Tanaka, K. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Nagai, Yuki Ota, Yukihiro Tanaka, K. |
| author_sort | Nagai, Yuki |
| collection | MIT |
| description | We solve the Bogoliubov-de Gennes equations self-consistently for the d-wave order parameter in nanoscale d-wave systems with [110] surfaces and show that spontaneous time-reversal symmetry (TRS) breaking occurs at low temperatures due to a spontaneously induced complex order parameter of extended s-wave symmetry. The Andreev surface bound states, which are protected by a one-dimensional (1D) topological invariant in the presence of TRS, are gapped by the emergence of this new order parameter. The extended s-wave order parameter is localized within a narrow region near the surfaces, which is consistent with the fact that topological protection of the gapless Andreev surface states is characterized by the 1D topological invariant. In this TRS-breaking phase, not only is the complex order parameter induced, but also the d-wave order parameter itself becomes complex. Furthermore, the disappearance of topological protection brings about novel vortex phenomena near the surfaces. We show that vortex-antivortex pairs are formed in the extended s-wave order parameter along the surfaces if the side length of a nanoisland or the width of an infinitely long nanoribbon is relatively large. |
| first_indexed | 2024-09-23T13:01:28Z |
| format | Article |
| id | mit-1721.1/110918 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:01:28Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1109182022-10-01T12:36:06Z Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands Nagai, Yuki Ota, Yukihiro Tanaka, K. Massachusetts Institute of Technology. Department of Physics Nagai, Yuki We solve the Bogoliubov-de Gennes equations self-consistently for the d-wave order parameter in nanoscale d-wave systems with [110] surfaces and show that spontaneous time-reversal symmetry (TRS) breaking occurs at low temperatures due to a spontaneously induced complex order parameter of extended s-wave symmetry. The Andreev surface bound states, which are protected by a one-dimensional (1D) topological invariant in the presence of TRS, are gapped by the emergence of this new order parameter. The extended s-wave order parameter is localized within a narrow region near the surfaces, which is consistent with the fact that topological protection of the gapless Andreev surface states is characterized by the 1D topological invariant. In this TRS-breaking phase, not only is the complex order parameter induced, but also the d-wave order parameter itself becomes complex. Furthermore, the disappearance of topological protection brings about novel vortex phenomena near the surfaces. We show that vortex-antivortex pairs are formed in the extended s-wave order parameter along the surfaces if the side length of a nanoisland or the width of an infinitely long nanoribbon is relatively large. 2017-08-03T14:24:03Z 2017-08-03T14:24:03Z 2017-08 2017-03 2017-08-02T22:00:07Z Article http://purl.org/eprint/type/JournalArticle 2469-9950 2469-9969 http://hdl.handle.net/1721.1/110918 Nagai, Yuki; Ota, Yukihiro andTanaka, K. "Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands." Physical Review B 96, 6 (August 2017): 060503(R) © 2017 American Physical Society en http://dx.doi.org/10.1103/PhysRevB.96.060503 Physical Review B 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 | Nagai, Yuki Ota, Yukihiro Tanaka, K. Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title | Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title_full | Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title_fullStr | Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title_full_unstemmed | Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title_short | Time-reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d-wave nanoislands |
| title_sort | time reversal symmetry breaking and gapped surface states due to spontaneous emergence of new order in d wave nanoislands |
| url | http://hdl.handle.net/1721.1/110918 |
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