  We use the density matrix renormalization group (DMRG) method to study the
SU(4) $t$-$J$ chain. We find that, in addition to the conventional repulsive
Luttinger liquid phase and phase separation, there are two phases in the
attractive Luttinger liquid region dependent on whether the flavor gap is
opened or not. The first with the flavor gap is the molecular superfluid phase
(the SU(4) singlet instability) which is well-known in the attractive SU(4)
Hubbard model ($U<0$). The second without the flavor gap is the superconducting
phase (the six-component pairing instability). Furthermore, the molecular
superfluid instability cannot coexist with the superconducting instability.
This is general in SU($N$) models with $N>2$ and is well demonstrated by the
theoretical analysis based on the phenomenological bosonization results.
