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

TL;DR

This paper uses a slave-spin formalism to study the $t-J-U$ model, revealing a doping-driven crossover from strong to weak pairing states in superconductors, with distinct effects for spin and charge interactions.

Contribution

It introduces a slave-spin mean-field approach to analyze the $t-J-U$ model, capturing the crossover between strong and weak pairing states based on the nature of interactions.

Findings

Doping-dependent crossover from strong to weak pairing states for spin interactions.

In strong pairing, $ ext{Delta}_f$ increases as doping decreases, but $ ext{Delta}_{SC}$ scales with doping.

For charge interactions, no crossover occurs; both gaps are suppressed at small doping.

Abstract

We investigate the superconductivity in the $t-J-U$ model within a slave-spin formalism. We show that the BCS mean-field theory implemented with the slave spin formalism naturally predicts two distinct gaps which are the pairing gap of 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 the interaction providing the pairing mechanism. For spin interactions, the bandwidth of the spinon hopping term is renormalized by $Z$ but the its pairing term is not. As a result, if $U$ exceeds the critical value for the Mott insulating state at half-filling, $Z$ develops a strong doping dependence, leading to a doping-driven crossover from strong to weak pairing states. In the strong pairing state, while $\Delta_f$ is enhanced as $x\to 0$, $\Delta_{SC}\sim x$ due to the renormalization of $Z$. In the weak pairing state, $Z$ does not change with $x$ significantly. Therefore, $\Delta_{SC}$ is mainly 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 slave spin formalism within reasonable range of parameters just at the mean-field level, indicating the slave spin formalism is a powerful tool to study correlated materials. For charge interactions, we find that the bandwidth of the spinon hopping term and its pairing term are renormalized by $Z$ and $Z^2$ respectively. Consequently, both $\Delta_f$ and $\Delta_{SC}$ are suppressed at small $x$ in large U, and no crossover will occur. The implication of our results for the superconducting states in correlated materials will be discussed.