The functional-integral approach to Gaussian fluctuations in Eliashberg theory
arXiv:2012.12287 · doi:10.1103/PhysRevB.104.014513
Abstract
The Eliashberg theory of superconductivity is based on a dynamical electron-phonon interaction as opposed to a static interaction present in BCS theory. The standard derivation of Eliashberg theory is based on an equation of motion approach, which incorporates certain approximations such as Migdal's approximation for the pairing vertex. In this paper we provide a functional-integral-based derivation of Eliashberg theory and we also consider its Gaussian-fluctuation extension. The functional approach enables a self-consistent method of computing the mean-field equations, which arise as saddle-point conditions, and here we observe that the conventional Eliashberg self energy and pairing function both appear as Hubbard-Stratonovich transformations. An important consequence of this fact is that it provides a systematic derivation of the Cooper and density-channel interactions in the Gaussian fluctuation response. We also investigate the strong-coupling fluctuation diamagnetic susceptibility near the critical temperature.
References in corpus (15)
- Diamagnetism and Cooper pairing above in cuprates
- Eliashberg Theory: a short review
- Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
- Pairing fluctuations and the superfluid density through the BCS-BEC crossover
- Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures
- Eliashberg theory of phonon-mediated superconductivity -- when it is valid and how it breaks down
- The low-energy phase-only action in a superconductor: a comparison with the XY model
- Gauge-invariant electromagnetic response of a chiral px+ipy superconductor
- Topological superfluid in a Fermi-Bose mixture with a high critical temperature
- Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors
- Towards exact solutions for the superconducting induced by electron-phonon interaction
- Kohn-Luttinger Correction to Tc in a Phonon Superconductor
- Correcting inconsistencies in the conventional superfluid path integral scheme
- Fluctuational Anomalous Hall and Nernst Effects in Superconductors
- Restoring gauge invariance in conventional fluctuation corrections to a superconductor