Band-basis decomposition of superfluid weight in magic-angle twisted bilayer graphene: Quantifying geometric and conventional contributions
Abstract
We decompose the superfluid weight Ds 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 Ds 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 Dsconv 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.
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