Mechanism of Superconductivity inGraphite Intercalation Compounds (GICs)
Takada GroupIn the study of the superconducting transition
temperature Tc by ab initio calculations, the ultimate
goal is to predict Tc by using only the information onelements composing superconductors. A lessambitious and yet very important goal is to make anaccurate estimation of Tc directly from a microscopic
Hamiltonian (in particular, without resort to theconcept of the Coulomb pseudopotential *), whichhelps us not only better understand the mechanism ofsuperconductivity but also obtain valuable hints tosynthesize a room-temperature superconductor.
In pursuit of the latter goal, a proposal was made in1978 for a scheme of calculating Tc directly from the
dynamic electron-electron effective interaction V(q, ),including both the phonon-mediated attraction and theCoulomb repulsion on the same footing [1]. The
scheme was successfully applied to the n-typesemiconducting SrTiO3 in which polar-coupledphonons leading to the stress-induced ferroelectrics
were clarified to play a crucial role [2]. This successhas assured us of both usefulness of this scheme andadequacy to employ the random-phase approximationin determining V(q, ) in the polar-phonon mechanism.
In 1982 this scheme was also successfully applied tothe alkali-doped GICs such as KC8 and RbC8 with Tc
in the range 0.01-0.1K by adopting such a model for
the GICs as schematically shown in Fig. 1 [3].

GIC superconductors or not, we have recently
calculated Tc based on exactly the same scheme [4].
The parameters in the model have been changed
appropriately for the new superconductors; forexample, we have used Z=2 instead of Z=1, m*~3me(due to the mixing of d electrons with the interlayerband) instead of m*=me (me: the mass of a freeelectron) and f = 0.16 (reflecting the stronger
attractive potential of M2+ for the interlayer band)
instead of f = 0.6. As shown in Fig. 2, we find that ourcalculations reproduce all the experimental results
quite well, implying that our model must be a standard
one representing all GIC superconductors with Tc
ranging more than three orders of magnitude. Our
calculations also reveal that the key parameters tocontrol Tc are Z and m*; the difference in Tc by twoorders between KC8 and CaC6 can be accounted for by(1) doubling Z, which enhances Tc by one order, and(2) tripling m*, which also enhances Tc by one order.

Fig. 2. Calculated Tc as a function of the branching ratio f. The
calculation is done from first principles based on the model inFig. 1 with using the band mass of the 3D electrons for m*. The
experimental result of Tc for each GIC is plotted at the value off determined by the band-structure calculation.

Fig. 1. In the GICs denoted by MCx, the metal element M is
ionized into MZ+ with Z the valence. The valence electrons
released from M go into either the two-dimensional (2D)-bands on the graphite layers or the three-dimensional (3D)interlayer band with the branching ratio of f : (1 - f). The 3D
electrons with the effective mass m* superconduct with theformation of the Cooper pairs mediated by the polarization
waves of ions.

In 2005, a breakthrough occurred in the field of theGIC superconductors. By changing alkali dopants into
alkaline-earth ones in synthesizing the GICs, Tc wasfound to be very much enhanced. In CaC6, forexample, Tc=11.5K, which was increased further to15.1K under pressures, and in YbC6, Tc=6.5K. Notethat Tc in CaC6 is about a hundred times higher thanthat in KC8, though the ion masses are about the same.
In order to check whether the same model in Fig. 1
applies to the newly-synthesized alkaline-earth-doped

Encouraged by this success and with confidence inthe predictive power of our standard model, we haveestimated the optimum Tc in the GIC superconductors
to find that Tc may become much higher than 10K, if
M is chosen as Ti or V. A further enhancement of Tc,
which might enter the range 50-100K, can be expected,
if two or more kinds of Ms are suitably intercalated, sothat both m* and Z are made large enough and thepolar-phonon energy is made as large as possible.
References[1] Y. Takada, J. Phys. Soc. Jpn. 45, 786 (1978).
[2] Y. Takada, J. Phys. Soc. Jpn. 49, 1267 (1980).
[3] Y. Takada, J. Phys. Soc. Jpn. 51, 63 (1982).
[4] Y. Takada, J. Phys. Soc. Jpn. 78, 013703 (2009).
AuthorY. Takada