Vertically Correlated Disorder and Structured Interlayer Tunneling in Cuprates

Cuprate superconductors display robust in-plane electronic correlations but exceptionally fragile interlayer coherence. We suggest that even weak vertically correlated disorder (arising from interstitial-oxygen staging, twin boundaries, extended strain fields, or defect-pinned charge textures) can impose a layer-dependent modulation of the interlayer tunneling amplitude t(z). Because the bare interlayer coupling is intrinsically small, such modulations generate an effectively multichannel c-axis electrodynamic response, consistent with multi-component Josephson plasma resonances, nonmonotonic c-axis resistivity, redistribution of bilayer magnetic spectral weight, and field-enhanced vertical CDW correlations. We propose a phenomenological framework in which the organization of disorder, rather than its magnitude, governs the effective interlayer coupling and its electrodynamic signatures. This viewpoint unifies diverse c-axis anomalies across several cuprate families, suggesting that controlling vertical disorder correlations offers a viable pathway for tuning dimensionality and interlayer coherence in high-Tc superconductors.