The role of Berry curvature derivatives in the optical activity of time-invariant crystals
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918017954217984 |
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| author | Soavi, Giancarlo Wilhelm, Jan |
| author_facet | Soavi, Giancarlo Wilhelm, Jan |
| contents | Quantum geometry and topology are fundamental concepts of modern condensed matter physics, underpinning phenomena ranging from the quantum Hall effect to protected surface states. The Berry curvature, a central element of this framework, is well established for its key role in electronic transport, whereas its impact on the optical properties of crystals remains comparatively unexplored. Here, we derive a relation between optical activity, defined by the gyration tensor, and the k-derivatives of the Berry curvature at optical resonances in the Brillouin zone. We systematically determine which of these derivatives are non-zero or constrained by symmetry across all time-reversal-invariant crystal classes. In particular, we analytically demonstrate that circular dichroism emerges in chiral crystal classes as a result of a non-zero Berry curvature k-derivative along the optical axis, and we interpret this finding based on the conservation of angular momentum in light-matter interactions. This work establishes a quantum-geometric framework for optical activity in solids and it opens new routes to probe quantum geometry via linear and nonlinear optics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The role of Berry curvature derivatives in the optical activity of time-invariant crystals Soavi, Giancarlo Wilhelm, Jan Mesoscale and Nanoscale Physics Optics Quantum geometry and topology are fundamental concepts of modern condensed matter physics, underpinning phenomena ranging from the quantum Hall effect to protected surface states. The Berry curvature, a central element of this framework, is well established for its key role in electronic transport, whereas its impact on the optical properties of crystals remains comparatively unexplored. Here, we derive a relation between optical activity, defined by the gyration tensor, and the k-derivatives of the Berry curvature at optical resonances in the Brillouin zone. We systematically determine which of these derivatives are non-zero or constrained by symmetry across all time-reversal-invariant crystal classes. In particular, we analytically demonstrate that circular dichroism emerges in chiral crystal classes as a result of a non-zero Berry curvature k-derivative along the optical axis, and we interpret this finding based on the conservation of angular momentum in light-matter interactions. This work establishes a quantum-geometric framework for optical activity in solids and it opens new routes to probe quantum geometry via linear and nonlinear optics. |
| title | The role of Berry curvature derivatives in the optical activity of time-invariant crystals |
| topic | Mesoscale and Nanoscale Physics Optics |
| url | https://arxiv.org/abs/2501.03684 |