Carbon isotope effect on the magic-angle superconducting transition temperature

For magic-angle devices built from 13C-enriched graphene, measure the isotope coefficient $\alpha_{\mathrm{iso}} = -d \ln T_c / d \ln M$ at fixed twist angle, filling and heterostrain, and compare it with the value each candidate mechanism predicts. For pairing by K-point optical phonons ($\hbar \omega \sim 0.15\,\mathrm{eV}$ $>> \text{ flat-band width}$ $W \sim 10\,\mathrm{meV}$) the anti-adiabatic regime can give $\alpha_{\mathrm{iso}}$ well below the BCS value 0.5; a purely electronic mechanism gives $\alpha_{\mathrm{iso}} \sim 0$. Since $\ln(13/12) = 0.08$, the answer is $\alpha_{\mathrm{iso}}$ with an error bar small enough to separate the computed predictions, which requires a statistical ensemble of devices.

Transport $T_c$ measured on ensembles of 12C and 13C magic-angle devices with matched angle and strain and quantified sample-to-sample scatter, compared with mechanism-specific calculations of $\alpha_{\mathrm{iso}}$ in the flat-band regime.