Quantum anharmonic effects and nonlinear electron-phonon coupling: beyond the standard approaches from first principles

The interplay between ionic fluctuations and electrons determines many physical phenomena, from thermodynamic and structural properties to transport and superconductivity. The harmonic approximation of ionic fluctuations  Notably, this second situation occurs in H-containing materials, where the large zero-point motion of the protons results in a violation of the harmonic approximation, even at low temperatures. We overcome the problem of taking into account quantum and anharmonic effects in nuclei dynamics by implementing a variational method for the nuclei problem that can be effectively employed in ab initio calculations: the stochastic self-consistent harmonic approximation (SSCHA) [1]. In this talk I will describe this method and I will show examples where its application allows to overcome the limitations of the standard approaches [2-6]. Moreover, when anharmonic effects are relevant, multi-phonon (i.e. nonlinear) processes can play a major role in the electron-phonon coupling too. In this talk I will present a method developed to take into account, from first principles, the effective nuclei-mediated electron-electron interaction so as to include nonlinear terms in the electron-phonon coupling at nonperturbative level. This method has been conceived to work in conjunction with SSCHA. I will also show preliminary results obtained within this method for PdH, a strongly anharmonic phonon-mediated superconductor for which a satisfactory first-principles description is still lacking [7].

[1] L. Monacelli, R. Bianco et al., J. Phys.: Condens. Matter 33, 363001 (2018)
[2] R. Bianco et al., Phys. Rev. B 97, 214101 (2018)
[3] R. Bianco et al., Nano Lett. 19, 3908 (2019)
[4] R. Bianco et al., Phys. Rev. Lett. 125, 106101 (2020)
[5] F. Belli et al., Nature 532, 81 (2020)
[6] U. Aseginolaza et al.,Phys. Rev. Lett. 122, 075901 (2019)
[7] I. Errea et al.,Phys. Rev. Lett. 111, 177002 (2013)       

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