1/2 Z Topological Invariants and the Half Quantized Hall Effect
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909323982012416 |
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| author | Fu, Bo Shen, Shun-Qing |
| author_facet | Fu, Bo Shen, Shun-Qing |
| contents | The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer $ν$ multiple of $e^{2}/h$. Here we demonstrate the existence of a novel $\frac{1}{2}\mathbb{Z}$ topological invariant that sets the half-quantized Hall phase apart from two-dimensional ordinary metallic ferromagnets. The $\frac{1}{2}\mathbb{Z}$ classification is determined by the line integral of the intrinsic anomalous Hall conductance, which is safeguarded by two distinct categories of local unitary and anti-unitary symmetries in proximity to the Fermi surface of electron states. We further validate the $\frac{1}{2}\mathbb{Z}$ topological order in the context of the quantized Hall phase by examining semi-magnetic topological insulator $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ and $\mathrm{Bi}_{2}\mathrm{Se}_{3}$ film for $ν=1$ and topological crystalline insulator SnTe films for $ν=2$ or $4$. Our findings pave the way for future exploration and understanding of topological metals and their unique properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15655 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 1/2 Z Topological Invariants and the Half Quantized Hall Effect Fu, Bo Shen, Shun-Qing Mesoscale and Nanoscale Physics The half-quantized Hall phase represents a unique metallic or semi-metallic state of matter characterized by a fractional quantum Hall conductance, precisely half of an integer $ν$ multiple of $e^{2}/h$. Here we demonstrate the existence of a novel $\frac{1}{2}\mathbb{Z}$ topological invariant that sets the half-quantized Hall phase apart from two-dimensional ordinary metallic ferromagnets. The $\frac{1}{2}\mathbb{Z}$ classification is determined by the line integral of the intrinsic anomalous Hall conductance, which is safeguarded by two distinct categories of local unitary and anti-unitary symmetries in proximity to the Fermi surface of electron states. We further validate the $\frac{1}{2}\mathbb{Z}$ topological order in the context of the quantized Hall phase by examining semi-magnetic topological insulator $\mathrm{Bi}_{2}\mathrm{Te}_{3}$ and $\mathrm{Bi}_{2}\mathrm{Se}_{3}$ film for $ν=1$ and topological crystalline insulator SnTe films for $ν=2$ or $4$. Our findings pave the way for future exploration and understanding of topological metals and their unique properties. |
| title | 1/2 Z Topological Invariants and the Half Quantized Hall Effect |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2409.15655 |