Generic reduction theory for Fermi sea topology in metallic systems
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912358218072064 |
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| author | Jia, Wei |
| author_facet | Jia, Wei |
| contents | The Fermi sea of a metal can host exotic quantum topology, which governs its conductance quantization and is characterized by the Euler characteristic ($χ_F$). In contrast to the well-known band topology, which is determined by the global features of wave functions, the topology of such metallic systems is intrinsically linked to the geometry of the Fermi sea. As a result, probing and identifying $χ_F$ in high-dimensional systems presents a challenge. Here, we propose a generic dimensional reduction theory for the Fermi sea topology in $d$-dimensional metallic systems, showing that $χ_F$ can be determined by the features of so-called reduced critical points on Fermi surfaces. Moreover, we reveal that $χ_F$ can be interpreted as a topological invariant of band topology by mapping a metallic system to a gapped system. Building on this nontrivial result, we identify a broad class of topological superconductors (SCs) whose topological numbers are precisely determined by the $χ_F$ of their normally filled bands. This provides an indirect method to capture $χ_F$ by measuring the (pseudo)spin polarizations of these topological SCs. Our findings are expected to significantly advance research into Fermi sea topology. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_19125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generic reduction theory for Fermi sea topology in metallic systems Jia, Wei Mesoscale and Nanoscale Physics Quantum Gases Superconductivity The Fermi sea of a metal can host exotic quantum topology, which governs its conductance quantization and is characterized by the Euler characteristic ($χ_F$). In contrast to the well-known band topology, which is determined by the global features of wave functions, the topology of such metallic systems is intrinsically linked to the geometry of the Fermi sea. As a result, probing and identifying $χ_F$ in high-dimensional systems presents a challenge. Here, we propose a generic dimensional reduction theory for the Fermi sea topology in $d$-dimensional metallic systems, showing that $χ_F$ can be determined by the features of so-called reduced critical points on Fermi surfaces. Moreover, we reveal that $χ_F$ can be interpreted as a topological invariant of band topology by mapping a metallic system to a gapped system. Building on this nontrivial result, we identify a broad class of topological superconductors (SCs) whose topological numbers are precisely determined by the $χ_F$ of their normally filled bands. This provides an indirect method to capture $χ_F$ by measuring the (pseudo)spin polarizations of these topological SCs. Our findings are expected to significantly advance research into Fermi sea topology. |
| title | Generic reduction theory for Fermi sea topology in metallic systems |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Superconductivity |
| url | https://arxiv.org/abs/2403.19125 |