Frequency Dependent Magnetic Susceptibility and the $q^2$ effective conductivity tensor
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866913774802305024 |
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| author | Duff, Alistair H. Sipe, J. E. |
| author_facet | Duff, Alistair H. Sipe, J. E. |
| contents | We apply a microscopic formalism for the calculation of material response properties to the problem of the generalization of a first-principles, i.e based on the energy spectrum and geometric properties of the Bloch functions, derivation of the AC magnetic susceptibility. We find that the AC susceptibility forms only a part of the $q^2$ -- where $q$ is the wavevector of the applied field -- effective conductivity tensor, and many additional response tensors characterizing both electric and magnetic multipole moments response to electromagnetic fields and their derivatives must be included to create the full gauge-invariant response. As was seen with the DC magnetic susceptibility and optical activity (characterized by the linear in $q$ contribution to the conductivity) one must be careful with the diagonal elements of the Berry connection. To our knowledge this is the only derivation of such a result general for crystalline insulators, with both `atomic like' contributions and `itinerant contributions' due to overlap of atomic orbitals and non-flat bands. Additionally, quantities familiar from quantum geometry like the Berry connection, curvature, and quantum metric appear extensively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frequency Dependent Magnetic Susceptibility and the $q^2$ effective conductivity tensor Duff, Alistair H. Sipe, J. E. Mesoscale and Nanoscale Physics We apply a microscopic formalism for the calculation of material response properties to the problem of the generalization of a first-principles, i.e based on the energy spectrum and geometric properties of the Bloch functions, derivation of the AC magnetic susceptibility. We find that the AC susceptibility forms only a part of the $q^2$ -- where $q$ is the wavevector of the applied field -- effective conductivity tensor, and many additional response tensors characterizing both electric and magnetic multipole moments response to electromagnetic fields and their derivatives must be included to create the full gauge-invariant response. As was seen with the DC magnetic susceptibility and optical activity (characterized by the linear in $q$ contribution to the conductivity) one must be careful with the diagonal elements of the Berry connection. To our knowledge this is the only derivation of such a result general for crystalline insulators, with both `atomic like' contributions and `itinerant contributions' due to overlap of atomic orbitals and non-flat bands. Additionally, quantities familiar from quantum geometry like the Berry connection, curvature, and quantum metric appear extensively. |
| title | Frequency Dependent Magnetic Susceptibility and the $q^2$ effective conductivity tensor |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2504.02215 |