Dynamical electron-phonon vertex correction
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908355137634304 |
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| author | Marini, Andrea |
| author_facet | Marini, Andrea |
| contents | The dynamical screening of the electron--phonon vertex is caused by the retarded oscillations of the electronic charge following the electron--hole scattering with a phonon mode. This retardation induces a frequency dependence of the electron--phonon interaction. Model Hamiltonians and {\em ab--initio} approaches have instilled the idea that this retardation is, in most of the cases, negligible. In this work I demonstrate that the dynamical screening of the electron--phonon vertex cannot be neglected {\em a priori}. By using a perturbative expansion I introduce a controllable and physically sound method to evaluate and include dynamical screening effects. Based on the exact results of the homogeneous electron gas I propose a dynamical vertex correction function $Γ_{e-p}(ω)$ designed to screen the commonly used adiabatic electron--phonon interaction. This function is expressed in terms of adiabatic quantities, that can be easily calculated and used to evaluate the strength of the dynamical corrections, even in realistic materials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_01866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical electron-phonon vertex correction Marini, Andrea Materials Science The dynamical screening of the electron--phonon vertex is caused by the retarded oscillations of the electronic charge following the electron--hole scattering with a phonon mode. This retardation induces a frequency dependence of the electron--phonon interaction. Model Hamiltonians and {\em ab--initio} approaches have instilled the idea that this retardation is, in most of the cases, negligible. In this work I demonstrate that the dynamical screening of the electron--phonon vertex cannot be neglected {\em a priori}. By using a perturbative expansion I introduce a controllable and physically sound method to evaluate and include dynamical screening effects. Based on the exact results of the homogeneous electron gas I propose a dynamical vertex correction function $Γ_{e-p}(ω)$ designed to screen the commonly used adiabatic electron--phonon interaction. This function is expressed in terms of adiabatic quantities, that can be easily calculated and used to evaluate the strength of the dynamical corrections, even in realistic materials. |
| title | Dynamical electron-phonon vertex correction |
| topic | Materials Science |
| url | https://arxiv.org/abs/2501.01866 |