Possibility of superconductivity in high pressure phases of BC$_3$*

Using an ab-initio pseudopotential-local-density-approximation, we study the possibility of a high-pressure transition of graphitic planar sp$^2$ bonded BC$_3$ into an sp$^3$ bonded covalent network. Energy barriers are examined for the predicted transition to the sp$^3$ phase and for the observed onset of phase separation in BC$_3$ under high pressure, high temperature conditions [V. L. Solozhenko \textit{et al.}, Appl. Phys. Lett. \textbf{85}, 1508 (2004)]. The sp$^3$ phase of BC$_3 $ is predicted to be metallic and superconducting and is similar to 25\% boron-doped diamond without boron clusters. Calculations of phonon frequencies and electron-phonon coupling allow for an estimate of the superconducting transition temperature.