Quantum critical fluctuations at a charge-density-wave transition in layered cuprates mediate Cooper pairing via a non-phonon boson exchange mechanism distinct from BCS theory

In hole-doped layered cuprate superconductors (e.g., YBa2Cu3O6+x, Bi2Sr2CaCu2O8+δ, La2-xBaxCuO4, Nd/Eu-LSCO) exhibiting a charge-density-wave (CDW) quantum critical point (QCP) near doping p* ≈ 0.16–0.19, quantum critical fluctuations of the CDW order parameter — not the superconducting phonon spectrum — provide the dominant pairing glue for Cooper pair formation in the superconducting dome surrounding that QCP. Specifically: (a) the pairing interaction strength λ(q,ω) derived from the CDW fluctuation propagator, extracted via RIXS/inelastic neutron/Raman susceptibility measurements, should reproduce the measured Tc(p) dome shape and the momentum-dependent (predominantly d-wave) superconducting gap Δ(k) within a factor of 2 using an Eliashberg-type or spin/charge-fluctuation-mediated pairing calculation with no phonon coupling term exceeding 20% of total λ; (b) this must hold quantitatively across at least 3 independent cuprate families; (c) isotope substitution (16O→18O) should produce Tc shifts consistent with negligible phonon contribution (α_iso < 0.05) in the doping regime closest to the CDW QCP, in contrast to larger conventional isotope effects elsewhere in the phase diagram.

Minimum viable test (MVT): Single-family, single-doping comparative study.

1. Select YBa2Cu3O6.67 (well-characterized CDW QCP-proximal doping, p≈0.12) as primary test material due to existing high-quality single crystals and extensive literature baseline.
2. Perform RIXS (Cu L3-edge) and/or inelastic neutron scattering to map CDW fluctuation spectrum Im χ_CDW(q,ω) across T = 4–300 K, focusing on (q_CDW,0) and (0,q_CDW) wavevectors.
3. Simultaneously perform ARPES to extract the electron self-energy Σ(k,ω) and identify coupling bosons via kink/waterfall analysis.
4. Compute pairing susceptibility λ_CDW from Im χ_CDW via McMillan-type integral; compare predicted Tc and gap Δ(k) against measured values (from ARPES gap maps, STM, specific heat).
5. Cross-check with 16O/18O isotope substitution Tc measurements on matched samples to bound phonon contribution independently.
6. Repeat steps 1–5 for Bi2212 and Nd-LSCO/Eu-LSCO (stripe-order family) to test cross-family generality.

for family in [YBCO, Bi2212, NdLSCO_EuLSCO]:
    for doping p in doping_series(family):
        sample = synthesize_or_procure(family, p, isotope_variants=[16O,18O])
        Tc[p] = measure_SQUID(sample)
        chi_CDW[p, q, omega, T] = measure_RIXS(sample, T_range, q_range)
        selfenergy[p, k, omega] = measure_ARPES(sample)
        gap_map[p, k] = extract_gap(selfenergy, STM_data(sample))

    alpha2F_ARPES[p] = invert_eliashberg(selfenergy[p])   # maximum entropy inversion
    alpha2F_RIXS[p]  = map_susceptibility_to_boson_spectrum(chi_CDW[p])  # charge-fluctuation exchange diagram

    agreement[p] = compare(alpha2F_ARPES[p], alpha2F_RIXS[p])  # peak pos, integrated lambda

    Tc_predicted_CDW[p] = solve_eliashberg(alpha2F_RIXS[p], coulomb_pseudopotential=mu_star)
    Tc_predicted_phonon[p] = solve_eliashberg(alpha2F_DFT_EPW[p])

    gap_predicted[p] = solve_gap_equation(alpha2F_RIXS[p], symmetry_channel='d-wave')

    error_CDW[p] = compare(Tc_predicted_CDW[p], Tc[p])
    error_phonon[p] = compare(Tc_predicted_phonon[p], Tc[p])

alpha_iso[p] = compute_isotope_exponent(Tc_16O[p], Tc_18O[p])

correlation_test = regress(Tc_max_doping_per_family, CDW_QCP_doping_per_family)

monte_carlo_uncertainty_propagation(n=1000, inputs=[chi_CDW, selfenergy], outputs=[Tc_predicted_CDW, gap_predicted])

decision = success_criteria_check(error_CDW, error_phonon, alpha_iso, agreement, correlation_test)