  We investigate the possibility of realizing unconventional superconductivity
in doped band insulators on the square lattice and the honeycomb lattice, where
the latter is found to be a good candidate due to the disconnectivity of the
Fermi surface. We propose applying the theory to the superconductivity in doped
layered nitride $\beta$-$M$NCl ($M=$Hf, Zr). Finally, we compare two groups of
superconductors with disconnected Fermi surface, $\beta$-$M$NCl and the iron
pnictides, which have high $T_c$ despite some faults against superconductivity
are present.
