Carbon isotope effect on the magic-angle superconducting transition temperature · revision history

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Title

Carbon isotope effect on the magic-angle superconducting transition temperature

Plain

Replacing carbon-12 by heavier carbon-13 slows the lattice vibrations, and the resulting shift of the superconducting transition temperature, compared with what each pairing theory predicts, would test whether phonons bind the pairs.

Precise

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 ($\hbar \omega \sim 0.15\,\mathrm{eV}$ >> flat-band width $W \sim 10\,\mathrm{meV}$) the anti-adiabatic regime can give alpha_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.

Settled by

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.

Kind

well-posed

Answer type

value

References

(empty)

Literature status

open

Status note

No measurement on isotope-enriched magic-angle devices is known to this survey as of 2026.

Posed since

(empty)