We propose a unified analytical framework bridging weakly coupled Bardeen-Cooper-Schrieffer (BCS) superconductivity and strongly correlated macroscopic quantum states. To resolve the finite-temperature thermodynamic paradox inherent in standard Gutzwiller projections, we embed the pairing wavefunction within a Slave-Boson Mean-Field Theory (SBMFT). By explicitly incorporating doping-scaled inter-layer coupling to satisfy the Mermin-Wagner theorem, we demonstrate thatfinite-temperature holon condensation remains thermodynamically rigorous. Combining the nearest-neighbor pairing boundary condition with the zero-integral constraint of the restricted Hilbert space, we analytically show that the B1g irreducible representation dₗℂ-ₘℂ-wave is the energetically and geometrically favored unique solution in the Mott limit. Furthermore, recognizing the inherent U (1) gauge fluctuations, we mathematically differentiate the Anderson-Higgs gapped superconducting state from the gapless pseudogap phase. Utilizing the Ioffe-Larkin rule and mapping holon dynamics onto Bardeen-Stephen vortex flow in the semi-classical limit, we derive the predictive AC microwave dissipation. Finally, we formulate a spatially dependent pinning functional for pancake vortices and derive a doping-gated anomalous isotope coefficient αₑff. Driven by the selective polaronic dressing of charged holons via anti-adiabatic timescale separation, this mechanism rigorously accounts for the anomalous isotope effect. Herein, we formally designate this overarching architecture as the Polaronic Fractionalization Model (PFM). The thermodynamic crossover between holon phase coherence and spinon pairing explicitly reproduces the full superconducting dome, providing robust predictive power that diverges fundamentally from generic weak-coupling models.
Hsinchuan Lin (Thu,) studied this question.