Phononic Self energy effects and superconductivity in CaC$_6$

TL;DR

This paper investigates the anisotropic electron-phonon interactions and polaronic effects in CaC$_6$ using Eliashberg theory, comparing with SCDFT to understand superconductivity and Coulomb interactions.

Contribution

It introduces a minimal 6-band anisotropic model and compares Eliashberg theory with SCDFT to analyze superconducting gap structures and Coulomb effects in CaC$_6$.

Findings

Eliashberg theory can reproduce SCDFT gap structures under certain conditions.

Polaronic quasiparticle bands exhibit anisotropic features.

Interplay between polaron effects and superconductivity is characterized.

Abstract

We study the graphite intercalated compound CaC$_6$ by means of Eliashberg theory, focusing on the anisotropy properties. An analysis of the electron-phonon coupling is performed, and we define a minimal 6-band anisotropy structure. Comparing with Superconducting Density Functional Theory (SCDFT) the condition under which Eliashberg theory is able to reproduce the SCDFT gap structure is determined, and we discuss the role of Coulomb interactions. The Engelsberg-Schrieffer polaron structure is computed by solving the Eliashberg equation on the Matsubara axis and analytically continuing it to the full complex plane. This reveals the polaronic quasiparticle bands anisotropic features as well as the interplay with superconductivity.