Phonons and superconductivity in ${\text{YbC}}_6$ and related compounds

The out-of-plane intercalate phonons of superconducting ${\text{YbC}}_6$ have been measured with inelastic x-ray scattering. Model fits to these data, and previously measured out-of-plane intercalate phonons in graphite intercalation compounds (GICs), reveal surprising trends with the superconducting transition temperature. These trends suggest that superconducting GICs should be viewed as electron-doped graphite.

Figure 1

(Color online) (a) The unit cell of ${\text{YbC}}_6$. Black hexagons represent graphene sheets and red solid circles represent Yb atoms. The black dashed lines represent the unit cell. The structure can be understood as graphene sheets separated by ordered intercalate layers. (b) A representative inelastic x-ray spectrum from ${\text{YbC}}_6$. The peak at zero energy loss is the elastic line. The features near 15 and 25 meV are out-of-plane ${\text{YbC}}_6$ phonons. The peak near 5 meV is from a phonon branch identified as in-plane ${\text{YbC}}_6$ phonons by comparison with calculations in Ref. 10.

Figure 2

(Color online) (a) A cartoon of the second–nearest-neighbor model used to fit the phonon dispersion. Black circles represent the graphene planes and red circles represent the Yb planes. The blue springs connect adjacent Yb and graphene planes, and the black and red springs connect graphene and Yb sheets to their nearest graphene or Yb neighbors. (b) $\left[00L\right]$ Phonon dispersion in ${\text{YbC}}_6$. The blue circles represent features assigned to out-of-plane intercalate phonons while the cyan squares represent features assigned to in-plane Yb phonons. The solid lines are a fit to the out-of-plane phonons with second-nearest-neighbor springs. (c) A cartoon of the bond charge model used to fit the phonon dispersion. The green stars represent electrons not strongly bound to either the graphene or Yb atoms. The spring constant between the electrons and Yb is labeled ${\text{K}}_{\text{e-i}}$ and the spring constant between the electrons and graphene is labeled ${\text{K}}_{\text{e-c}}$. (d) $\left[00L\right]$ Phonon dispersion in ${\text{YbC}}_6$. The solid lines are a fit to the out-of-plane phonons with the bond charge model. (e) A cartoon of the shell model. The unfilled circles represent the electron shells around the ion cores. The ion cores are tethered to the center of their electron shells by springs with spring constants ${\text{K}}_{\text{i}}$ or ${\text{K}}_{\text{C}}$. The shells are connected to each other with springs with spring constants ${\text{K}}_{\text{S-S}}$. The fit from the shell model is indistinguishable from the fit with the bond charge mode, shown in Fig. 2d.

Figure 3

(Color online) (a) Fit results from ${\text{YbC}}_6$ and a number of different GICs. In the first panel, the spring constant connecting the graphene sheets to the bond charge is shown. The units are $\mu \text{N}/{\text{m}}^3$ when considering mass per area. The dotted line is a guide to the eyes. (b) The spring constant connecting the intercalate sheets to the bond charge is shown. Note that there is over a factor of 4 difference between the highest and lowest spring constants.