Theory 003/Physics & Matter /Condensed matter
Moiré Superconductivity Peaks at Integer Filling
The dome is drawn as a smooth curve. The peaks may sit at integer fillings like steps.
Superconductivity in twisted bilayers peaks when the moiré unit cell contains an integer number of electrons, so the phase diagram is set by a commensurability condition rather than by a smooth density optimum.
01The evidence
Twisted bilayer superconductivity appears in a dome as a function of filling, with maxima near integer fillings of the moiré band in several material systems.
02The tension
The dome is modelled as a smooth function of density, which predicts a single maximum and cannot explain why maxima appear at several fillings with dips between them.
03The mechanism
At integer filling the moiré superlattice is commensurate with the electron density, so umklapp scattering and interaction effects are enhanced coherently. Between integers the coherence is frustrated.
If commensurability sets the pairing, then the phase diagram should show a sequence of peaks at integers, with the strongest at the filling where the flat band is half filled and interactions are strongest.
04What this is not
Density-dome models predict one maximum. This predicts a comb of maxima at integer fillings.
05Predictions
- P1Peaks should sit at integer fillings across twist angles.
- P2Dips should appear between integers.
- P3The strongest peak should track the half-filled flat band.
06Refutation
A single smooth maximum across fillings would refute the commensurability condition.
07What it changes
It would make filling a design variable in moiré materials.