  Superstructures of cubic and hexagonal diamonds (h- and c-diamond) comprising
a family of stable diamond-like $sp^3$ hybridized novel carbon allotropes are
proposed, which are referred to as U$_n$-carbon where $n \geq 2$ denotes the
number of structural layers in a unit cell. The conventional h- and c-diamond
are included in this family as members with $n=2$ and 3, respectively.
U$_n$-carbon ($n=4-6$), which are unveiled energetically and thermodynamically
more stable than h-diamond and possess remarkable kinetic stabilities, are
shown to be insulators with indirect gaps of $5.6 \sim 5.8$ eV, densities of $
3.5 \sim 3.6$ g/cm$^3$, bulk modulus of $4.3 \sim 4.4 \times 10^{2}$ GPa, and
Vickers hardness of $92.9 \sim 97.5$ GPa even harder than h- and c-diamond. The
simulated x-ray diffraction and Raman spectra are presented for experimental
characterization. These new structures of carbon would have a compelling impact
in physics, chemistry, materials science and geophysics.
