First-principles theory of nonlinear long-range electron-phonon interaction
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arXiv
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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909615506063360 |
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| author | Houtput, Matthew Ranalli, Luigi Verdi, Carla Klimin, Serghei Ragni, Stefano Franchini, Cesare Tempere, Jacques |
| author_facet | Houtput, Matthew Ranalli, Luigi Verdi, Carla Klimin, Serghei Ragni, Stefano Franchini, Cesare Tempere, Jacques |
| contents | Describing electron-phonon interactions in a solid requires knowledge of the electron-phonon matrix elements in the Hamiltonian. State-of-the-art first-principles calculations for the electron-phonon interaction are limited to the 1-electron-1-phonon matrix element, which is suitable for harmonic materials. However, there is no first-principles theory for 1-electron-2-phonon interactions, which occur in anharmonic materials with significant electron-phonon interaction such as halide perovskites and quantum paraelectrics. Here, we derive an analytical expression for the long-range part of the 1-electron-2-phonon matrix element, written in terms of microscopic quantities that can be calculated from first principles. We show that the long-range 1-electron-2-phonon interaction is described by the derivative of the phonon dynamical matrix with respect to an external electric field. We calculate the quasiparticle energy of a large polaron including 1-electron-2-phonon interaction, and show that it can be written in terms of a 1-electron-2-phonon spectral function $\mathcal{T}_{αβ}(ω)$. We demonstrate how to calculate this spectral function and its temperature dependence for the benchmark materials LiF and KTaO$_3$, where it turns out that the effect is very small. The first-principles framework developed in this article is general, paving the way for future calculations of 1-electron-2-phonon interactions in materials where the effect may be larger. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_09470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | First-principles theory of nonlinear long-range electron-phonon interaction Houtput, Matthew Ranalli, Luigi Verdi, Carla Klimin, Serghei Ragni, Stefano Franchini, Cesare Tempere, Jacques Materials Science Describing electron-phonon interactions in a solid requires knowledge of the electron-phonon matrix elements in the Hamiltonian. State-of-the-art first-principles calculations for the electron-phonon interaction are limited to the 1-electron-1-phonon matrix element, which is suitable for harmonic materials. However, there is no first-principles theory for 1-electron-2-phonon interactions, which occur in anharmonic materials with significant electron-phonon interaction such as halide perovskites and quantum paraelectrics. Here, we derive an analytical expression for the long-range part of the 1-electron-2-phonon matrix element, written in terms of microscopic quantities that can be calculated from first principles. We show that the long-range 1-electron-2-phonon interaction is described by the derivative of the phonon dynamical matrix with respect to an external electric field. We calculate the quasiparticle energy of a large polaron including 1-electron-2-phonon interaction, and show that it can be written in terms of a 1-electron-2-phonon spectral function $\mathcal{T}_{αβ}(ω)$. We demonstrate how to calculate this spectral function and its temperature dependence for the benchmark materials LiF and KTaO$_3$, where it turns out that the effect is very small. The first-principles framework developed in this article is general, paving the way for future calculations of 1-electron-2-phonon interactions in materials where the effect may be larger. |
| title | First-principles theory of nonlinear long-range electron-phonon interaction |
| topic | Materials Science |
| url | https://arxiv.org/abs/2412.09470 |