2001: Hexagonal s-p Superconductors:

S-p superconductors have a common crystal structure, shown above; hexagonal planes of boron, carbon (Al,Si), are intercalated by alkali atoms or alkaline earths.
The first member of this class to attract attention was MgB2, where superconductivity with Tc=39 K was discovered in 2001. Within two years, thanks mostly to DFT calculations, it was understood that the high superconducting temperature of MgB2 is caused by a strong interaction between sigma electrons and bond-stretching phonons.
Despite an intense theoretical and experimental search, a higher Tc has still not been found, but several new superconductors with the same crystal structure have been synthesized.
We have used linear-response calculations method to calculate their electron-phonon interaction and critical temperaturesand the NMTO downfolding method to unravel their electronic properties. We have shown that the basic electronic structure of all these compounds can be understood in term of that of simple graphite. Intercalating the graphitic planes with other atoms changes the relative positions of the bands and their filling. Depending on which electronic states sit at the Fermi level, different electron-phonon interactions will result.
- Doping with holes (MgB2) triggers a strong electron-phonon interaction between sigma bands and bond-stretching phonons.
- Doping with electrons (intercalated graphites[1], CaAlSi[2]) brings at the Fermi level interlayer states, which interact with pi states via out-of-plane phonons.
- LiB, a material designed "ab-initio", has both sigma and interlayer states at the Fermi level. However, its predicted critical temperature is lower than that of MgB2.[3]

References:

[1] J. S. Kim, L. Boeri, R. K. Kremer, and F. S. Razavi, Effect of pressure on superconducting Ca-intercalated graphite CaC6, Phys. Rev. B 74, 214513 (2006).
L. Boeri, G. B. Bachelet, M. Giantomassi, and O. K. Andersen, "Electron-phonon interaction in graphite intercalation compounds", Phys. Rev. B 76, 064510 (2007);
J. S. Kim, L. Boeri, J. R. O'Brien, F. S. Razavi, and R. K. Kremer, "Superconductivity in Heavy Alkaline-Earth Intercalated Graphites", Phys. Rev. Lett. 99, 027001 (2007).
[2] M. Giantomassi, L. Boeri, G.B. Bachelet, "Electrons and phonons in the ternary alloy CaAl2–xSix as a function of composition , Phys. Rev. B 72, 224512 (2005);
L. Boeri, J. S. Kim, M. Giantomassi,2 F. S. Razavi,3 S. Kuroiwa,4 J. Akimitsu,4 and R. K. Kremer, " Pressure effects on the superconducting transition in nH–CaAlSi", Phys. Rev. B 77, 144502 (2008).
[3]A. N. Kolmogorov and S. Curtarolo, Phys. Rev. B 74, 224507 (2006); A. Y. Liu and I. I. Mazin, Phys. Rev. B 75, 064510 (2007); M. Calandra, A. N. Kolmogorov, and S. Curtarolo Phys. Rev. B 75, 144506 (2007).