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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2604.07806 |
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| _version_ | 1866917397931229184 |
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| author | Li, Hua-Yu Tan, Hengxin Zhu, Hao-Yu Yuan, Hong-Kuan Kuang, Min-Quan |
| author_facet | Li, Hua-Yu Tan, Hengxin Zhu, Hao-Yu Yuan, Hong-Kuan Kuang, Min-Quan |
| contents | Van Hove singularities (VHSs) play a pivotal role in driving correlated electronic phenomena. Traditional classifications focus only on critical points where the band gradient vanishes in all directions. Here we establish a unified classification of VHSs in three-dimensional systems, characterized by the number of vanishing gradient components and Hessian eigenvalues: ordinary ($M$-type), higher-order ($T_1$, $T_2$, $T_3$), noncritical ordinary ($N_0$, $N_1$, $N_2$), and noncritical higher-order ($S_1$, $S_2$) types. Noncritical VHSs exhibit directional quenching: the gradient vanishes in a two-dimensional subspace while remaining finite along the orthogonal direction, yielding finite density-of-states enhancements with distinct energy dependencies. Using an $s$-orbital tight-binding model on the pyrochlore lattice with spin-orbit coupling, we demonstrate that all singularity classes emerge at distinct high-symmetry points through controlled tuning of the hopping ratio. This work establishes directional criticality and higher-order flatness as design principles for tailoring density-of-states enhancements in three-dimensional quantum materials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07806 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Directional Criticality and Higher-Order Flatness: Designing Van Hove Singularities in Three Dimensions Li, Hua-Yu Tan, Hengxin Zhu, Hao-Yu Yuan, Hong-Kuan Kuang, Min-Quan Strongly Correlated Electrons Materials Science Van Hove singularities (VHSs) play a pivotal role in driving correlated electronic phenomena. Traditional classifications focus only on critical points where the band gradient vanishes in all directions. Here we establish a unified classification of VHSs in three-dimensional systems, characterized by the number of vanishing gradient components and Hessian eigenvalues: ordinary ($M$-type), higher-order ($T_1$, $T_2$, $T_3$), noncritical ordinary ($N_0$, $N_1$, $N_2$), and noncritical higher-order ($S_1$, $S_2$) types. Noncritical VHSs exhibit directional quenching: the gradient vanishes in a two-dimensional subspace while remaining finite along the orthogonal direction, yielding finite density-of-states enhancements with distinct energy dependencies. Using an $s$-orbital tight-binding model on the pyrochlore lattice with spin-orbit coupling, we demonstrate that all singularity classes emerge at distinct high-symmetry points through controlled tuning of the hopping ratio. This work establishes directional criticality and higher-order flatness as design principles for tailoring density-of-states enhancements in three-dimensional quantum materials. |
| title | Directional Criticality and Higher-Order Flatness: Designing Van Hove Singularities in Three Dimensions |
| topic | Strongly Correlated Electrons Materials Science |
| url | https://arxiv.org/abs/2604.07806 |