Superconducting length scales such as the coherence length and penetration depth are fundamental to the characterization of superconductors, as they govern critical fields, currents, and electromagnetic response. Despite their central role, these quantities are rarely accessed in theoretical studies, particularly in strongly correlated materials. Here, we introduce a general framework to compute these length scales from microscopic theories by tracking the response of the superconducting state to finite pairing momentum. This approach allows the coherence length, penetration depth, and also depairing current to be extracted on equal footing within a single formalism.

Applying this method to conventional superconductors, we obtain quantitative agreement with experimentally measured length scales across elemental, A15, and hydride materials using superconducting density functional theory [1]. This includes predictions for depairing currents, offering a microscopic benchmark for values that remain challenging to access experimentally. Turning to strongly correlated superconductivity in alkali-doped fullerides (A3C60), we use dynamical mean-field theory to identify a regime where the interplay of strong correlations and multiorbital effects stabilizes a strong local-pair superconducting state [2]. Our approach reveals that this regime is characterized by elevated critical temperatures and robust stiffness despite short coherence lengths.
Together, these results establish a route toward a more complete microscopic characterization of superconductors, providing a foundation for the predictive modeling of complex superconducting materials.

[1] M. Kawamura et al., arXiv:2603.05123
[2] N. Witt et al., npj Quantum Materials 9, 100 (2024); doi:10.1038/s41535-024-00706-7