  Motivated by superconductivity (SC) in layered nitrides, we study an
ionic-Hubbard model on a honeycomb lattice, which consists of two sublattices
with an energy-level offset, by using an optimization variational Monte Carlo
method. Parameter values for the Coulomb interaction and the energy-level
offset, to realize a band insulator in non-doped state, are evaluated, and the
SC state is investigated in a carrier-doped band insulator. It is found that,
in a weakly doped band insulator, spin fluctuation remains and the spin-singlet
d-wave SC state is realized. Present results support an unconventional
spin-singlet SC state suggested by the experimental observations in layered
nitrides.
