Structural and electronic properties of Li- and Cu-doped β-rhombohedral boron constructed from icosahedral and truncated icosahedral clusters

This study performs dc conductivity and static magnetic-susceptibility measurements on Li- and Cu-doped β-rhombohedral boron (β-rhombohedral B), which is a unique polymorphic semiconducting (group III) material composed of ${\mathrm{B}}_{12}$ icosahedral clusters. dc conductivity results show a variable-range-hopping (VRH)-type temperature dependence with a typical localization length of about ∼1 Å. In addition, the density of states (DOS) at the Fermi energy, which is calculated from fitted parameters of VRH conduction, was found to have a peak with respect to metal concentration, such that at the highest concentration (${\mathrm{Li}}_{7.9}$ ${\mathrm{B}}_{105}$ and ${\mathrm{Cu}}_{4.2}$ ${\mathrm{B}}_{105}$), metal-doped β-rhombohedral B appears to revert back to an insulator, instead of showing insulator-to-metal transition. Corresponding static magnetic-susceptibility results, however, show a contribution from Pauli paramagnetism in the temperature-independent component ${\mathrm{\chi }}_0$, where a similar concentration dependence is shows to that in the DOS of VRH conduction. Based on these properties, we discuss the possibility of filling the intrinsic acceptor band, which originates from the uppermost molecular bonding orbital of the ${\mathrm{B}}_{12}$ icosahedral cluster that is split by the Jahn-Teller effect. β-rhombohedral B’s crystalline structure can also be viewed as a slightly distorted face-centered cubic (fcc) packing of ${\mathrm{B}}_{84}$ soccer-ball-shaped clusters covalently bound to each other and containing a relatively large number of large-size interstitial doping sites. This structure is considered to be topologically similar to that of fcc ${\mathrm{C}}_{60}$, although the bonding mechanisms of their clusters are different, and therefore we also describe the similarities and differences between them.