Superconductivity is like a dance of electrons: they move in pairs without losing energy. In conventional superconductors, this dance is set by the electron velocity. But in magic-angle graphene — two carbon sheets twisted relative to each other by 1.1 degrees — electrons almost freeze, and their supercurrent, as it turned out, relies on something else: quantum geometry.
Quantum geometry is not about the shape of the sheet but about how electron wavefunctions are arranged: their mutual orientation in the space of states. The researchers applied to the magic-angle graphene model a method that splits the supercurrent contribution into two parts: the conventional one (from electron velocity) and the geometric one (from interband coherence). At neutral charge, the geometric part accounted for 22–26% depending on pairing symmetry, and with the inclusion of remote energy bands it grew to 55–58%.
Practical value: understanding the role of quantum geometry opens the way to designing new superconductors with tailored properties that operate at higher temperatures. If the geometric contribution can be enhanced, we might obtain materials that conduct electricity without loss at room temperature.
as written by the authors arXiv:2604.05994
We decompose the superfluid weight D_s of magic-angle twisted bilayer graphene (MATBG) into conventional (band-velocity) and geometric (interband-coherence) contributions using a band-basis current operator splitting applied to the Bistritzer-MacDonald continuum model. In the flat-band subspace, quantum geometry accounts for 22-26% of D_s at charge neutrality depending on pairing symmetry, with cross terms vanishing to machine precision. Including remote bands raises the geometric fraction to ~55-58%, while D_s^conv converges to within 2% -- demonstrating that remote bands contribute exclusively through interband coherence. The geometric fraction peaks at ~27-33% near the nu = +/- 2 fillings where superconductivity is strongest, and is insensitive to gap magnitude in the experimentally relevant range.
The magic angle of 1.1 degrees is like fine-tuning strings: at the slightest deviation, superconductivity disappears.