Flat-band superconductivity and quantum geometry

3 problems

• Quantitative test of geometric superfluid stiffness in moire superconductors

  Partially resolved

  Measurements since 2023 found that the superconducting pairs in magic-angle graphene are far stiffer than the slow electron speed allows, which points to quantum geometry, but a quantitative match to theory has not been made.

• Linear scaling of $T_c$ with attraction in isolated flat bands

  Open

  For flat bands theory predicts a superconducting temperature proportional to the pairing attraction, much larger than the exponentially small value of ordinary metals when the attraction is weak, and no experiment has tested this scaling directly.

• Direct measurement of the quantum metric of moire flat bands

  Open

  The quantum metric measures how fast electron wavefunctions change across momentum space and is central to flat-band theories, but it has not been measured for the flat bands of moire graphene.