Orbital magnetization from parallel transport of Bloch states
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909952962985984 |
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| author | Mitscherling, Johannes Priessnitz, Jan Šmejkal, Libor |
| author_facet | Mitscherling, Johannes Priessnitz, Jan Šmejkal, Libor |
| contents | Quantum geometric formulations of linear and nonlinear responses can be constructed from a single building block in the form of a gauge-invariant interband transition operator. Here, we identify a second building block for quantum geometry: a band-resolved adiabatic connection operator that captures the noncommutativity between band projectors and their momentum derivatives. The band-resolved adiabatic connection operator, first introduced in the theory of adiabatic driving, serves as a generalized angular momentum within the state manifold of single bands, and we employ it to reformulate expressions for the band-resolved orbital magnetic moment. This form provides a complementary geometric interpretation alongside the multiband separation between energetic- and quantum-state properties by the two-state Berry curvature. Our formalism allows us to present formulas valid for both nondegenerate and degenerate bands, thereby removing the limitations of the common Bloch-state formula. We illustrate our theory by calculating a large orbital magnetization emerging without spin-orbit coupling in a spin-compensated, noncoplanar anomalous Hall magnet with degenerate bands. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_09051 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbital magnetization from parallel transport of Bloch states Mitscherling, Johannes Priessnitz, Jan Šmejkal, Libor Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons Quantum geometric formulations of linear and nonlinear responses can be constructed from a single building block in the form of a gauge-invariant interband transition operator. Here, we identify a second building block for quantum geometry: a band-resolved adiabatic connection operator that captures the noncommutativity between band projectors and their momentum derivatives. The band-resolved adiabatic connection operator, first introduced in the theory of adiabatic driving, serves as a generalized angular momentum within the state manifold of single bands, and we employ it to reformulate expressions for the band-resolved orbital magnetic moment. This form provides a complementary geometric interpretation alongside the multiband separation between energetic- and quantum-state properties by the two-state Berry curvature. Our formalism allows us to present formulas valid for both nondegenerate and degenerate bands, thereby removing the limitations of the common Bloch-state formula. We illustrate our theory by calculating a large orbital magnetization emerging without spin-orbit coupling in a spin-compensated, noncoplanar anomalous Hall magnet with degenerate bands. |
| title | Orbital magnetization from parallel transport of Bloch states |
| topic | Mesoscale and Nanoscale Physics Materials Science Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.09051 |