Effect of the boundary on thermodynamic quantities such as magnetization
In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization, and the magnetoelectric tensor are affected by the boundaries. We show that when the calculation with periodic boundary conditions does not involve a Berry's phase, the quantity in que...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2014
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| Online Access: | http://hdl.handle.net/1721.1/88732 https://orcid.org/0000-0001-7809-8157 |
| _version_ | 1826210068007223296 |
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| author | Chen, Kuang-Ting Lee, Patrick A. |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Chen, Kuang-Ting Lee, Patrick A. |
| author_sort | Chen, Kuang-Ting |
| collection | MIT |
| description | In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization, and the magnetoelectric tensor are affected by the boundaries. We show that when the calculation with periodic boundary conditions does not involve a Berry's phase, the quantity in question is determined unambiguously by the bulk, even in the presence of gapless surface states. When the calculation involves a Berry's phase, the bulk can only determine the quantity up to some quantized value, given that (i) there are no gapless surface states, (ii) the surfaces do not break the symmetries preserved by the bulk, and (iii) the system is kept at charge neutrality. If any of the above conditions is violated, the quantity is then determined entirely by the details at the boundary. Due to the strong dependence on the boundary, this kind of thermodynamic quantity, such as the isotropic magnetoelectric coefficient, cannot be measured in the bulk without careful control at the boundary. One thus cannot distinguish between a topological insulator and a trivial insulator in three dimensions by any local measurement in the bulk. |
| first_indexed | 2024-09-23T14:41:44Z |
| format | Article |
| id | mit-1721.1/88732 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:41:44Z |
| publishDate | 2014 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/887322022-09-29T10:08:54Z Effect of the boundary on thermodynamic quantities such as magnetization Chen, Kuang-Ting Lee, Patrick A. Massachusetts Institute of Technology. Department of Physics Chen, Kuang-Ting Lee, Patrick A. In this paper, we investigate in general how thermodynamic quantities such as the polarization, magnetization, and the magnetoelectric tensor are affected by the boundaries. We show that when the calculation with periodic boundary conditions does not involve a Berry's phase, the quantity in question is determined unambiguously by the bulk, even in the presence of gapless surface states. When the calculation involves a Berry's phase, the bulk can only determine the quantity up to some quantized value, given that (i) there are no gapless surface states, (ii) the surfaces do not break the symmetries preserved by the bulk, and (iii) the system is kept at charge neutrality. If any of the above conditions is violated, the quantity is then determined entirely by the details at the boundary. Due to the strong dependence on the boundary, this kind of thermodynamic quantity, such as the isotropic magnetoelectric coefficient, cannot be measured in the bulk without careful control at the boundary. One thus cannot distinguish between a topological insulator and a trivial insulator in three dimensions by any local measurement in the bulk. National Science Foundation (U.S.) (Grant DMR 1104498) 2014-08-15T17:52:07Z 2014-08-15T17:52:07Z 2012-11 2012-07 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/88732 Chen, Kuang-Ting, and Patrick A. Lee. “Effect of the Boundary on Thermodynamic Quantities Such as Magnetization.” Phys. Rev. B 86, no. 19 (November 2012). © 2012 American Physical Society https://orcid.org/0000-0001-7809-8157 en_US http://dx.doi.org/10.1103/PhysRevB.86.195111 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. application/pdf American Physical Society American Physical Society |
| spellingShingle | Chen, Kuang-Ting Lee, Patrick A. Effect of the boundary on thermodynamic quantities such as magnetization |
| title | Effect of the boundary on thermodynamic quantities such as magnetization |
| title_full | Effect of the boundary on thermodynamic quantities such as magnetization |
| title_fullStr | Effect of the boundary on thermodynamic quantities such as magnetization |
| title_full_unstemmed | Effect of the boundary on thermodynamic quantities such as magnetization |
| title_short | Effect of the boundary on thermodynamic quantities such as magnetization |
| title_sort | effect of the boundary on thermodynamic quantities such as magnetization |
| url | http://hdl.handle.net/1721.1/88732 https://orcid.org/0000-0001-7809-8157 |
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