Zeros of Green functions in topological insulators
This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-06-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.023177 |
| _version_ | 1827285459309428736 |
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| author | Takahiro Misawa Youhei Yamaji |
| author_facet | Takahiro Misawa Youhei Yamaji |
| author_sort | Takahiro Misawa |
| collection | DOAJ |
| description | This study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials. |
| first_indexed | 2024-04-24T10:15:06Z |
| format | Article |
| id | doaj.art-5bc8c94c90f44c43af62d35199b97570 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:15:06Z |
| publishDate | 2022-06-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-5bc8c94c90f44c43af62d35199b975702024-04-12T17:21:30ZengAmerican Physical SocietyPhysical Review Research2643-15642022-06-014202317710.1103/PhysRevResearch.4.023177Zeros of Green functions in topological insulatorsTakahiro MisawaYouhei YamajiThis study demonstrates that the zeros of the diagonal components of Green functions are key quantities that can detect noninteracting topological insulators. We show that zeros of the Green functions traverse the band gap in the topological phases. The traverses induce the crosses of zeros, and the zeros' surface in the band gap, analogous to the Fermi surface of metals. By calculating the zeros of the microscopic models, we show the traverses of the zeros universally appear in all six classes of conventional noninteracting topological insulators. By utilizing the eigenvector-eigenvalue identity, which is a recently rediscovered relation in linear algebra, we prove that the traverses of the zeros in the bulk Green functions are guaranteed by the band inversions, which occur in the topological phases. The relevance of the zeros to detecting the exotic topological insulators such as the higher-order topological insulators is also discussed. For the Hamiltonians with the nearest-neighbor hoppings, we also show that the gapless edge state guarantees the zeros' surfaces in the band gap. The analysis demonstrates that the zeros can be used to detect a wide range of topological insulators and thus useful for searching new topological materials.http://doi.org/10.1103/PhysRevResearch.4.023177 |
| spellingShingle | Takahiro Misawa Youhei Yamaji Zeros of Green functions in topological insulators Physical Review Research |
| title | Zeros of Green functions in topological insulators |
| title_full | Zeros of Green functions in topological insulators |
| title_fullStr | Zeros of Green functions in topological insulators |
| title_full_unstemmed | Zeros of Green functions in topological insulators |
| title_short | Zeros of Green functions in topological insulators |
| title_sort | zeros of green functions in topological insulators |
| url | http://doi.org/10.1103/PhysRevResearch.4.023177 |
| work_keys_str_mv | AT takahiromisawa zerosofgreenfunctionsintopologicalinsulators AT youheiyamaji zerosofgreenfunctionsintopologicalinsulators |