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We propose a comprehensive theoretical formulation of magnetic penetrationdepth, $\lambda(T)$, based on the microscopic calculations for a generalsuperconducting gap symmetry. Our findings admit the significant role of bandstructure and Fermi surface topology together with the symmetry ofsuperconducting order parameter. We employ our findings pertaining to theheavy-fermion superconductor CeCoIn$_5$ to explore both local and non-localbehaviors in response to an external magnetic field across varyingtemperatures. Our calculations in the low-temperature regime offer compellingmacroscopic evidence of the nodal character within the superconducting statewith $d_{x^2-y^2}$ symmetry. Furthermore, our findings align with thecharacteristics of London-type superconductivity, holding significantimplications for upcoming experiments.

Microscopic Insights into London Penetration Depth: Application to CeCoIn$^{}_{5}$