Electronic structures and superconductivity of endohedrally dopedC28solids from first principles

Abstract

We present ab initio calculations of the crystalline phases of ${\mathrm{C}}_{28}$: hyperdiamond and hyperlonsdaleite, in their pristine and endohedrally doped forms. These are hard materials with strong covalent bonds between the ${\mathrm{C}}_{28}$ molecules, and yet their electronic properties have remarkable similarities to the weakly bonded ${\mathrm{C}}_{28}{\mathrm{H}}_{4}$ molecular solids previously investigated [Phys. Rev. B 70, 140504(R) (2004)]. Our calculations show that they exhibit very narrow bands near the Fermi energy with an electron-phonon coupling that is well described by a molecular model and is larger than in ${\mathrm{C}}_{60}$. Our study focuses on ${\mathrm{C}}_{28}$ solids endohedrally doped with Zr, a group-IVB tetravalent atom. Solid $\mathrm{Zr}@{\mathrm{C}}_{28}$ is a small-gap insulator with Jahn-Teller distortions. Since the two structures considered are degenerate in energy, the actual material is expected to have disorder affecting the states at the Fermi energy and leading to a nonvanishing density of states. We conclude that the small density of states at the Fermi energy for $\mathrm{Zr}@{\mathrm{C}}_{28}$ will lead to a superconducting transition temperature ${T}_{c}$ lower than that found in ${\mathrm{K}}_{3}{\mathrm{C}}_{60}$; however, our results suggest that a higher ${T}_{c}$ may be obtained using group-IIIB trivalent atoms.