Fermi-surface calculation of the anomalous Hall conductivity
While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its "nonquantized part") may alternatively...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797056273933402112 |
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| author | Wang, X Vanderbilt, D Yates, JR Souza, I |
| author_facet | Wang, X Vanderbilt, D Yates, JR Souza, I |
| author_sort | Wang, X |
| collection | OXFORD |
| description | While the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its "nonquantized part") may alternatively be expressed as a Fermi-surface property. Here we present an ab initio approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally localized Wannier functions are then constructed by a postprocessing step in order to convert the ab initio electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co, and Ni. © 2007 The American Physical Society. |
| first_indexed | 2024-03-06T19:21:03Z |
| format | Journal article |
| id | oxford-uuid:1a19a7f0-dfec-4442-b737-0c74f4117d0b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T19:21:03Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:1a19a7f0-dfec-4442-b737-0c74f4117d0b2022-03-26T10:52:51ZFermi-surface calculation of the anomalous Hall conductivityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1a19a7f0-dfec-4442-b737-0c74f4117d0bEnglishSymplectic Elements at Oxford2007Wang, XVanderbilt, DYates, JRSouza, IWhile the intrinsic anomalous Hall conductivity is normally written in terms of an integral of the electronic Berry curvature over the occupied portions of the Brillouin zone, Haldane has recently pointed out that this quantity (or more precisely, its "nonquantized part") may alternatively be expressed as a Fermi-surface property. Here we present an ab initio approach for computing the anomalous Hall conductivity that takes advantage of this observation by converting the integral over the Fermi sea into a more efficient integral on the Fermi surface only. First, a conventional electronic-structure calculation is performed with spin-orbit interaction included. Maximally localized Wannier functions are then constructed by a postprocessing step in order to convert the ab initio electronic structure around the Fermi level into a tight-binding-like form. Working in the Wannier representation, the Brillouin zone is sampled on a large number of equally spaced parallel slices oriented normal to the total magnetization. On each slice, we find the intersections of the Fermi-surface sheets with the slice by standard contour methods, organize these into a set of closed loops, and compute the Berry phases of the Bloch states as they are transported around these loops. The anomalous Hall conductivity is proportional to the sum of the Berry phases of all the loops on all the slices. Illustrative calculations are performed for Fe, Co, and Ni. © 2007 The American Physical Society. |
| spellingShingle | Wang, X Vanderbilt, D Yates, JR Souza, I Fermi-surface calculation of the anomalous Hall conductivity |
| title | Fermi-surface calculation of the anomalous Hall conductivity |
| title_full | Fermi-surface calculation of the anomalous Hall conductivity |
| title_fullStr | Fermi-surface calculation of the anomalous Hall conductivity |
| title_full_unstemmed | Fermi-surface calculation of the anomalous Hall conductivity |
| title_short | Fermi-surface calculation of the anomalous Hall conductivity |
| title_sort | fermi surface calculation of the anomalous hall conductivity |
| work_keys_str_mv | AT wangx fermisurfacecalculationoftheanomaloushallconductivity AT vanderbiltd fermisurfacecalculationoftheanomaloushallconductivity AT yatesjr fermisurfacecalculationoftheanomaloushallconductivity AT souzai fermisurfacecalculationoftheanomaloushallconductivity |