Selfconsistent theory of superconductivity in unconventional superconductors

Abstract: Superconductivity is broadly believed to stem from either electron-phonon interaction (EPI) or from purely electronic mechanisms, such as antiferromagnetic spin fluctuations. For many materials the discussion about which of these interactions is the dominant "pairing glue" is still ongoing. This is particularly the case for unconventional superconductors, such as the high-Tc cuprates, where the origin of superconductivity is still not known after 30 years of intense research.This thesis, which is split into two parts, aims at contributing to unveiling the role of these Cooper pairing mediators in unconventional superconductors by applying a powerful state-of-the-art method, self-consistent calculations on the basis of Eliashberg's theory.In the first part we employ Eliashberg theory under Migdal's approximation for the electron-phonon interaction, and apply a similar level of approximation for spin fluctuations. For monolayer FeSe on SrTiO3, the record holder for Tc in Fe-based superconductors, we show that EPI is responsible for the large critical temperature and key spectral features, while spin fluctuations induce an unconventional symmetry of the superconducting order parameter. For the recently discovered superconductor Twisted Bilayer Graphene we explain the main characteristics of the superconducting state by assuming isotropic EPI, and predict various spectral features, which are expected to be measurable in tunneling experiments. We further discuss superconductivity in high-pressure materials as atomic metallic hydrogen and LaH10, introduce a numerical method for making Eliashberg calculations more efficient, and give an overview of possible effects due to phonon renormalization.The second part of the thesis emphasizes the role of EPI in unconventional superconductors. By deriving a self-consistent set of Eliashberg equations beyond Migdal's approximation, we show that isotropic EPI causes unconventional symmetries of the superconducting gap in three representative examples, the Fe-based, cuprate and heavy fermion superconductors. Therefore, our results prove that unconventional order parameters are not a sufficient criterion to assume purely electronic mechanisms, and establish conventional EPI as potential mediator of superconductivity. With the Fe-based compound ThFeAsN we identify a real physical system in which such effects might play an important role. We conclude by presenting an induced subordinate odd-frequency superconducting state that coexists with its primary even-frequency counterpart, solely due to vertex corrections beyond Migdal's approximation in a cuprate model system.

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