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Electron-phonon and phonon-electron coupling

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The impact of atomic vibration on electronic properties (electron-phonon coupling) and the impact of dynamical electronic motion on the atomic vibration (phonon-electron coupling) are crucial to describe many phenomena including carrier mobility, phonon-assisted superconductivity, temperature dependence of the bandgaps, electron mass enhancement, Kohn anomalies and phonon softening. The predictive calculation of these effects has been made possible thanks to recent advances in perturbative first-principles simulation of the electron-phonon coupling [1,2].

In this presentation, I will first discuss the Allen-Heine-Cardona theory for the renormalization of the electronic bandstructure with temperature and show that the adiabatic theory breaks down in infrared-active materials [3].

I will then present the Boltzmann transport equation within the general framework of the quantum theory of mobility [4]. I will subsequently discuss the accuracy limit of ab initio electron-phonon calculations of carrier mobilities and show that predictive calculations of electron and hole mobilities require an extremely fine sampling of inelastic scattering processes in momentum space. Such fine sampling calculation is made possible at an affordable computational cost through the use of efficient Fourier-Wannier interpolation of the electron-phonon matrix elements [2]. In addition, recent advances have allowed for the extension of the theory to the realms of 2D materials [5].

Finally, I will show how the phonon self-energy can be efficiently and accurately used to study the fine features of Kohn anomalies by using two adiabatically screened vertices due to designed error cancellation to first order [6].

[1] X. Gonze et al., Comput. Phys. Commun. 248, 107042 (2020). [2] H. Lee et al., npj Comput. Mater. 9, 156 (2023). [3] S. Poncé et al., J. Chem. Phys. 143, 102813 (2015). [4] S. Poncé et al., Rep. Prog. Phys. 83, 036501 (2020). [5] S. Poncé et al., Phys. Rev. Lett. 130, 166301 (2023). [6] J. Berges et al., Phys. Rev. X 13 , 041009 (2023).

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