  The $t\!\!-\!\!J$ Hamiltonian is one of the cornerstones in the theoretical
study of strongly correlated copper-oxide based materials. Using the density
matrix renormalization group method we calculate the phase diagram of the
one-dimensional (1D) $t\!\!-\!\!J$ chain in the presence of a periodic hopping
modulation, as a prototype of coupled-segment models. While in the uniform 1D
$t\!\!-\!\!J$ model near half-filling superconducting (SC) state dominates only
at unphysically large values of the exchange coupling constant $J/t>3$, we show
that a small hopping and exchange modulation very strongly reduces the critical
coupling to be as low as $J/t\sim1/3$ -- well within the physical regime. The
phase diagram as a function of the electron filling also exhibits metallic,
insulating line phases and regions of phase separation. We suggest that a SC
state is easily stabilized if $t\!\!-\!\!J$ segments creating local
spin-singlet pairing are coupled to each other -- another example is ladder
system.

Superconductivity