Nonlinear electron-phonon interactions in Migdal-Eliashberg theory
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915306953244672 |
|---|---|
| author | Zappacosta, Ingvar Houtput, Matthew Tempere, Jacques |
| author_facet | Zappacosta, Ingvar Houtput, Matthew Tempere, Jacques |
| contents | Superconducting systems based on attractive electron-phonon interactions are the ones which are best understood at a fundamental level. They are well described using Eliashberg theory, which, unlike BCS theory, explicitly takes into account phonon dynamics. It is most often assumed that only linear electron-phonon interactions are relevant. However, for some superconductors like MgB$_2$ or hydride based superconductors, nonlinear electron-phonon interactions are known to contribute significantly, which is not taken into account in conventional Eliashberg theory. We provide a modification to Eliashberg theory by introducing nonlinear electron-phonon interactions. We show that the Eliashberg equations remain unchanged apart from a nonlinear extension of the Eliashberg spectral function. This extended spectral function can be used as a baseline for future ab initio calculations. We use it to construct an analytical toy model and show that the nonlinear electron-phonon coupling affects the superconducting gap function on the imaginary and real axis and causes an increase in the superconducting critical temperature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear electron-phonon interactions in Migdal-Eliashberg theory Zappacosta, Ingvar Houtput, Matthew Tempere, Jacques Superconductivity Superconducting systems based on attractive electron-phonon interactions are the ones which are best understood at a fundamental level. They are well described using Eliashberg theory, which, unlike BCS theory, explicitly takes into account phonon dynamics. It is most often assumed that only linear electron-phonon interactions are relevant. However, for some superconductors like MgB$_2$ or hydride based superconductors, nonlinear electron-phonon interactions are known to contribute significantly, which is not taken into account in conventional Eliashberg theory. We provide a modification to Eliashberg theory by introducing nonlinear electron-phonon interactions. We show that the Eliashberg equations remain unchanged apart from a nonlinear extension of the Eliashberg spectral function. This extended spectral function can be used as a baseline for future ab initio calculations. We use it to construct an analytical toy model and show that the nonlinear electron-phonon coupling affects the superconducting gap function on the imaginary and real axis and causes an increase in the superconducting critical temperature. |
| title | Nonlinear electron-phonon interactions in Migdal-Eliashberg theory |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2503.04560 |