Topological Classification of Crystalline Insulators through Band Structure Combinatorics
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-u...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2017-12-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.7.041069 |
| _version_ | 1818985333631483904 |
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| author | Jorrit Kruthoff Jan de Boer Jasper van Wezel Charles L. Kane Robert-Jan Slager |
| author_facet | Jorrit Kruthoff Jan de Boer Jasper van Wezel Charles L. Kane Robert-Jan Slager |
| author_sort | Jorrit Kruthoff |
| collection | DOAJ |
| description | We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K-theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A. Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases. |
| first_indexed | 2024-12-20T18:33:14Z |
| format | Article |
| id | doaj.art-cbafeeafdc3048e5a81abb33799e8e84 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-20T18:33:14Z |
| publishDate | 2017-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-cbafeeafdc3048e5a81abb33799e8e842022-12-21T19:30:00ZengAmerican Physical SocietyPhysical Review X2160-33082017-12-017404106910.1103/PhysRevX.7.041069Topological Classification of Crystalline Insulators through Band Structure CombinatoricsJorrit KruthoffJan de BoerJasper van WezelCharles L. KaneRobert-Jan SlagerWe present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm applies to crystals without time-reversal, particle-hole, chiral, or any other anticommuting or anti-unitary symmetries. The results presented match the mathematical structure underlying the topological classification of these crystals in terms of K-theory and therefore elucidate this abstract mathematical framework from a simple combinatorial perspective. Using a straightforward counting procedure, we classify all allowed topological phases of spinless particles in crystals in class A. Employing this classification, we study transitions between topological phases within class A that are driven by band inversions at high-symmetry points in the first Brillouin zone. This enables us to list all possible types of phase transitions within a given crystal structure and to identify whether or not they give rise to intermediate Weyl semimetallic phases.http://doi.org/10.1103/PhysRevX.7.041069 |
| spellingShingle | Jorrit Kruthoff Jan de Boer Jasper van Wezel Charles L. Kane Robert-Jan Slager Topological Classification of Crystalline Insulators through Band Structure Combinatorics Physical Review X |
| title | Topological Classification of Crystalline Insulators through Band Structure Combinatorics |
| title_full | Topological Classification of Crystalline Insulators through Band Structure Combinatorics |
| title_fullStr | Topological Classification of Crystalline Insulators through Band Structure Combinatorics |
| title_full_unstemmed | Topological Classification of Crystalline Insulators through Band Structure Combinatorics |
| title_short | Topological Classification of Crystalline Insulators through Band Structure Combinatorics |
| title_sort | topological classification of crystalline insulators through band structure combinatorics |
| url | http://doi.org/10.1103/PhysRevX.7.041069 |
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