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We investigate the superconductivity in the $t-J-U$ model within a slave-spinformalism. We show that the BCS mean-field theory implemented with the slavespin formalism naturally predicts two distinct gaps which are the pairing gapof the spinons $\Delta_f$ and the Cooper pairing gap of the electrons$\Delta_{SC} = Z\Delta_f$, where $Z$ is the quasiparticle weight. Furthermore,we find that the nature of the superconducting state depends crucially on theinteraction providing the pairing mechanism. For spin interactions, thebandwidth of the spinon hopping term is renormalized by $Z$ but the its pairingterm is not. As a result, if $U$ exceeds the critical value for the Mottinsulating state at half-filling, $Z$ develops a strong doping dependence,leading to a doping-driven crossover from strong to weak pairing states. In thestrong pairing state, while $\Delta_f$ is enhanced as $x\to 0$,$\Delta_{SC}\sim x$ due to the renormalization of $Z$. In the weak pairingstate, $Z$ does not change with $x$ significantly. Therefore, $\Delta_{SC}$ ismainly controlled by $\Delta_f$, and both of them go to zero at larger doping.The crossover from strong to weak pairing states is well captured by the slavespin formalism within reasonable range of parameters just at the mean-fieldlevel, indicating the slave spin formalism is a powerful tool to studycorrelated materials. For charge interactions, we find that the bandwidth ofthe spinon hopping term and its pairing term are renormalized by $Z$ and $Z^2$respectively. Consequently, both $\Delta_f$ and $\Delta_{SC}$ are suppressed atsmall $x$ in large U, and no crossover will occur. The implication of ourresults for the superconducting states in correlated materials will bediscussed.

Crossover From Strong to Weak Pairing States in $t-J-U$ Model Studied by A Slave Spin Method