Guided by a simple strategy in search of new superconducting materials, we predict that high-temperature superconductivity can be realized in classes of high-density materials having strong ${\mathit{sp}}^3$ chemical bonding and high lattice symmetry. We examine in detail sodalite carbon frameworks doped with simple metals such as Li, Na, and Al. Though such materials share some common features with doped diamond, their doping level is not limited, and the density of states at the Fermi level in them can be as high as that in the renowned $\mathrm{Mg}{\mathrm{B}}_2$. Together with other factors, this boosts the superconducting temperature $\left(T_c\right)$ in the materials investigated to higher levels compared to doped diamond. For example, the $T_c$ of sodalitelike $\mathrm{Na}{\mathrm{C}}_6$ is predicted to be above 100 K. This phase and a series of other sodalite-based superconductors are predicted to be metastable phases but are dynamically stable. Owing to the rigid carbon framework of these and related dense carbon materials, these doped sodalite-based structures could be recoverable as potentially useful superconductors.

• Received 20 November 2015
• Revised 16 December 2015

DOI:https://doi.org/10.1103/PhysRevB.93.104509