  Boson-fermion mixture exist in nature as quark-gluon plasma and $^3$He-$^4$He
mixture. We proposed a convective boson-fermion pairing theory, that can be
implemented by ultracold atoms in optical superlattice transformation between
different configurations. This transformation may induce the collision and
division between boson and fermion, which defines a theoretical convective
pairing state. The paring Hamiltonian is Hermitian but it always generate a
complex energy spectrum. Each finite gap state can be classified by a
topological winding number. The stable pairing state only exists for certain
discrete momentum vector zones. An unstable linear dispersion connects two
neighboring stable pairing states. The boson-fermion gap function controls the
momentum gap space between two neighboring pairing state. The critical
temperature of transition from a gapped to gapless phase shows a maximal value
at negative fermion chemical potential. The density of state for the pairing
excitation diverges at low energy, thus most pairing states are observable at
low energy.
