Superconductivity in twisted graphene is probed by tunneling spectroscopy and superfluid stiffness, two observables that access the same order parameter from complementary perspectives. We show that a finite-momentum pair-density-wave (PDW) state, consistent with reported Kekul\'e signatures, reconciles substantial low-energy tunneling weight with an approximately T2 suppression of the low-temperature superfluid stiffness. The PDW order produces a Bogoliubov Fermi surface and finite zero-bias conductance. The same gapless quasiparticles also enter the geometric superfluid response, yielding a low-temperature stiffness suppression that persists in the flat-band limit. We further predict that, under density or displacement-field tuning, enhanced residual zero-bias conductance should accompany reduced low-temperature stiffness, providing a direct experimental link between tunneling spectroscopy and phase rigidity in twisted graphene.
@article{arxiv.2603.24766,
title = {Geometric superfluid stiffness of Kekul\'e superconductivity in magic-angle twisted bilayer graphene},
author = {Ke Wang and Qijin Chen and Rufus Boyack and K. Levin},
journal= {arXiv preprint arXiv:2603.24766},
year = {2026}
}