Topological edge states of massless fermion with non-quantized and zero Berry phases
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911933392748544 |
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| author | Pratama, F. R. Nakanishi, Takeshi |
| author_facet | Pratama, F. R. Nakanishi, Takeshi |
| contents | We investigate the bulk-boundary correspondence for massless Dirac fermion in $α$-${T}_3$ lattice where the Berry phase can be continuously tuned from $π$ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by unitary transform of the Hamiltonian, which maps $α$-${T}_3$ zigzag ribbon (ZR) into stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the $\mathbb{Z}_2$ invariant is manifested by azimuthal winding numbers on the Bloch sphere. Particularly, $T_3$ ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to the conventional topological insulators, band gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17914 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological edge states of massless fermion with non-quantized and zero Berry phases Pratama, F. R. Nakanishi, Takeshi Mesoscale and Nanoscale Physics We investigate the bulk-boundary correspondence for massless Dirac fermion in $α$-${T}_3$ lattice where the Berry phase can be continuously tuned from $π$ (graphene) to $0$ ($T_3$ or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by unitary transform of the Hamiltonian, which maps $α$-${T}_3$ zigzag ribbon (ZR) into stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the $\mathbb{Z}_2$ invariant is manifested by azimuthal winding numbers on the Bloch sphere. Particularly, $T_3$ ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to the conventional topological insulators, band gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition. |
| title | Topological edge states of massless fermion with non-quantized and zero Berry phases |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2406.17914 |