Flux Phase in Bilayer $t-J$ Model (1409.0661v5)

Abstract: In order to study the time-reversal symmetry (${\cal T}$) breaking near a (110) surface of a high-$T_C$ cuprate YBCO, we consider the flux phase in a bilayer $t-J$ model. Although the stable solution in the bulk is the $d_{x^2-y-2}$-wave superconducting (SC) state, free energy of the flux phase is close to it, and thus the flux phase may occur when the SC order is disturbed by inhomogeneity, e.g., surface or impurity. It is found that, depending on the doping rate, the flux phase in which spontaneous magnetic fields in two layers have opposite signs may be stabilized. This may lead to a surface state with local ${\cal T}$ violation but without local magnetic field.

• The paper demonstrates that a flux phase emerges in the bilayer t-J model, identifying Type A and Type B states influenced by doping levels.
• The research employs a slave-boson mean-field approximation to analyze intralayer and interlayer dynamics, aligning theoretical predictions with experimental observations.
• The findings explain how counter-propagating currents in the Type B state cancel magnetic fields, offering deeper insights into symmetry breaking in high-TC superconductors.

Flux Phase in Bilayer $t$-$J$ Model

The paper presented in "Flux Phase in Bilayer $t-J$ Model" investigates the emergence of a flux phase within the context of bilayer high-$T_C$ cuprate superconductors, particularly through the lens of the $t$-$J$ model. The research addresses the time-reversal symmetry (${\cal T}$) breaking in high-$T_C$ superconductors, a phenomenon supported by various experiments, but whose underlying mechanisms remain contentious.

Theoretical Framework

The analysis centers on a bilayer $t-J$ model structured on a square lattice. The Hamiltonian is divided into intralayer terms for each layer and an interlayer term. The model considers both intralayer and interlayer transfer integrals, alongside the antiferromagnetic superexchange interactions. The presence of staggered currents and the resulting flux phases are studied under the constraints of no double occupancy, handled using the slave-boson mean-field (MF) approximation.

In addressing the flux phase, the model distinguishes between two derived phases: Type A and Type B flux states. These classifications consider the directions in which flux might penetrate different layers, either aligned or opposing, which significantly influences the resultant magnetic fields.

Key Findings and Numerical Results

Numerical evaluation identifies that the transition temperature to the flux phase ($T_{FL}$) is closely linked with the doping rate and exhibits a critical feature where Type B flux phase is predominant for doping rates $\delta \lesssim 0.15$. The phenomenological parameters chosen align with experimental observations, providing both qualitative and quantitative insights into the critical doping rate $\delta_c$ in the bilayer system. Here, $\delta_c$ aligns with observed results, demonstrating the model's concordance with experimental high-$T_C$ behaviors.

One notable outcome is the Type B phase's tendency to induce counter-propagating currents in layers that cancel each other's magnetic effects, explaining the lack of macroscopic magnetic field evidence in some experiments. This finding underscores the importance of considering bilayer coupling effects and their inferences on magnetic properties in superconductors.

Practical and Theoretical Implications

The paper's implications extend to understanding the microscopic causalities behind symmetry-breaking phenomena in cuprate superconductors. By employing a bilayer model, the research significantly refines the predictive accuracy regarding $T_{FL}$ and extends the applicability of the $t$-$J$ model in explaining high-$T_C$ superconductivity. Furthermore, the results suggest reconsidering incommensurate orders in inhomogeneous systems, offering pathways to integrating more complex order parameters in future modeling efforts.

Conclusion

"Flux Phase in Bilayer $t-J$ Model" enhances the comprehension of bilayer coupling effects and the associated flux phase dynamics in high-$T_C$ cuprates. By focusing on the intricate interplay of interlayer and intralayer dynamics, the research furnishes a more nuanced understanding of superconducting order suppression near surfaces. Future explorations may incorporate sophisticated computational tools like BdG calculations to further elucidate local electronic structure influences and potentially resolve remaining experimental discrepancies.