Induced Representation Method in the Theory of Electron Structure and Superconductivity
It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/4873914 |
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| author | V. G. Yarzhemsky |
| author_facet | V. G. Yarzhemsky |
| author_sort | V. G. Yarzhemsky |
| collection | DOAJ |
| description | It is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered. |
| format | Article |
| id | doaj-art-a42310a7259e409294145a32d9e0b3e6 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a42310a7259e409294145a32d9e0b3e62025-02-03T01:00:14ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/48739144873914Induced Representation Method in the Theory of Electron Structure and SuperconductivityV. G. Yarzhemsky0Kurnakov Institute of General and Inorganic Chemistry, 31 Leninsky Prospect, 119991 Moscow, RussiaIt is shown that the application of theorems of induced representations method, namely, Frobenius reciprocity theorem, transitivity of induction theorem, and Mackey theorem on symmetrized squares, makes simplifying standard techniques in the theory of electron structure and constructing Cooper pair wavefunctions on the basis of one-electron solid-state wavefunctions possible. It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. The technique is extended on projective representations in the case of nonsymmorphic space groups and examples of applications for topological superconductors UPt3 and Sr2RuO4 are considered.http://dx.doi.org/10.1155/2019/4873914 |
| spellingShingle | V. G. Yarzhemsky Induced Representation Method in the Theory of Electron Structure and Superconductivity Advances in Mathematical Physics |
| title | Induced Representation Method in the Theory of Electron Structure and Superconductivity |
| title_full | Induced Representation Method in the Theory of Electron Structure and Superconductivity |
| title_fullStr | Induced Representation Method in the Theory of Electron Structure and Superconductivity |
| title_full_unstemmed | Induced Representation Method in the Theory of Electron Structure and Superconductivity |
| title_short | Induced Representation Method in the Theory of Electron Structure and Superconductivity |
| title_sort | induced representation method in the theory of electron structure and superconductivity |
| url | http://dx.doi.org/10.1155/2019/4873914 |
| work_keys_str_mv | AT vgyarzhemsky inducedrepresentationmethodinthetheoryofelectronstructureandsuperconductivity |