Band-basis decomposition of superfluid weight in magic-angle twisted bilayer graphene: Quantifying geometric and conventional contributions

TL;DR

This paper decomposes the superfluid weight in magic-angle twisted bilayer graphene into geometric and conventional parts, revealing the significant role of quantum geometry and remote bands in superconductivity.

Contribution

It introduces a band-basis current operator splitting method to quantify geometric and conventional contributions to superfluid weight in MATBG, highlighting remote bands' impact.

Findings

Quantum geometry accounts for 22-26% of superfluid weight at charge neutrality.

Including remote bands increases the geometric contribution to about 55-58%.

The geometric fraction peaks near the fillings where superconductivity is strongest.

Abstract

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.