Figure 1

Three-band FS resolved ${\alpha }^2{F}_{J{J}^{\prime }}\left(\omega \right)$ of CaC${}_6$. The three panels refer to the incoming FS, from which the electron is scattered, while the three lines in each panel refer to the outgoing FS.Reuse & Permissions

Figure 2

(a) Anisotropy of the superconducting gap in the three-band FS approximation and (b) six-band FS approximation. In (a), the dark green thick line is used for the gap computed over FS 1; the blue thin line for the gap computed over FS 2; and the red dashed line for gap computed over FS 3. In (b), dark green thick and dotted thin lines are used for 1a and 1b FS, respectively; blue thin and dash-dotted thick lines for 2a and 2b FS, respectively; and red dashed thick and dashed thin lines for 3a and 3b FS, respectively. (a) and (b) refer to phonon only calculations. Inset (c) shows the effect of the inclusion of the Coulombic interaction: the Eliashberg $T_c$ is given as a function of ${\mu }^{*}$ (see text for details). Inset (d) reports the low-temperature multigap structure for ${\mu }^{*}=0.21$. Panels (e) and (f) report the gap distribution functions (phonon only calculations) in the six-band FS approximation in SCDFT (Ref. 24) and Eliashberg theory (with a Gaussian broadening applied), respectively.Reuse & Permissions

Figure 3

Eliashberg functions. (a) Superconducting gap and mass renormalization function calculated solving the isotropic Eliashberg equations on the imaginary axis. (b) Analytically continued gap function on the real axis. (c) Analytically continued mass renormalization function on the real axis. Full lines are used for the real part and dashed lines for the imaginary part of these complex functions. On the imaginary axis, the functions are purely real.Reuse & Permissions

Figure 4

Polaronic bands and spectral function for the normal state in the isotropic approximation. On panel (a), the polaronic quasiparticle dispersion curves are shown. This is obtained from the real and imaginary parts of the solution of Eq. (14). The inverse lifetime of the state is given by $\left|\text{Im}\right(z_p\left)\right|$ and it is reported for some points as “error bar.” Panel (b) shows the spectral function $A(k,\omega )$. The abscissa represents the $\left|\mathbf{k}\right|$ axis, and the point in which $A(k,\omega )$ crosses is ${\mathbf{k}}_F$. In the ordinate, the frequency axis is reported. The color scale goes from zero to about 15 eV${}^{-1}$ [note that we cut it off to enhance the structures of $A(k,\omega )$]. Panel (c) shows $A(k,\omega )$ for different values of the momentum. A few values are highlighted and correspond to $\mathbf{k}$ values indicated in panel (b). Panel (d) shows ${\alpha }^{2}F\left(\omega \right)$ computed in the the isotropic one-band approximation.Reuse & Permissions

Figure 5

Polaronic bands and spectral function for the anisotropic and superconducting states of CaC${}_6$ determined within the six-band approximation. The central panel shows the band structure of CaC${}_6$: the continuous green line is the C$\pi$ band corresponding to FS 1; the blue dotted-dashed line is the Ca interlayer band corresponding to FS 2; and the red dashed line is the second C$\pi$ band corresponding to FS 3 (see Table for plots of the several FS portions). Further subdivisions are not reported explicitly. Panels (a) to (i) show the spectral function near the Fermi energy in a wide energy window of $300\text{meV}$. The letters correspond to the labeling of the crossing points in the central panel. The color scale goes from zero (black) to 15 eV${}^{-1}$ (white). Higher peaks in the spectral function have been cut off. Panels with a primed index show the quasiparticle spectrum (see text for details). These also show the polaronic branches together with the main electronic band. Colors are proportional to the linewidth of the quasiparticle state: black corresponds to zero and yellow/white correspond to about $0.1\text{eV}$. Panels (b${}^{*}$), (c${}^{*}$), (f${}^{*}$), and (h${}^{*}$), focusing on the superconducting gap (a logarithmic color scale is used), show a zoom of the spectral function near the Fermi energy in a narrow energy window of $20\text{meV}$. Panel (c${}^{\#}$) is the same as (c${}^{*}$) but evaluated in the nonsuperconducting state.Reuse & Permissions