Beyond minimal coupling for charged scalars? Modified electrodynamics and London-penetration tests

Abstract

We discuss an effective modification of the electromagnetic coupling for charged scalar condensates. The motivation is not an inconsistency of standard scalar QED, but a semiclassical tension: for scalar fields the term linear in $A_\mu$ is not itself the conserved source current of the interacting theory, while for Dirac fields the usual interaction already has the form $-A_\mu J^\mu$ with an $A_\mu$-independent conserved current. We review this distinction, clarify the effective-theory status of the alternative coupling, and state explicitly the corresponding limitations: the framework is not proposed as a UV-complete replacement of gauge theory and standard Ward identities or scattering-theory results should not be expected to survive unchanged. We then focus on the condensed-matter consequence relevant to superconductors. For bosonic charged condensates the modified framework predicts a rescaled magnetic penetration depth, $\lambda_{\rm mag}=\lambda_L/\sqrt{2}$, while leaving the qualitative structure of AC electrodynamics and the type-I/type-II classification unchanged up to parameter mapping. Finally, we compare literature values of an ``optical'' penetration depth $\lambda_{\rm opt}$, inferred from optical/THz superfluid spectral weight, with independently determined magnetic lengths $\lambda_{\rm mag}$ for Nb, Pb, YBCO, MgB$_2$ and Ba(Fe,Co)$_2$As$_2$. The present data do not constitute a proof of the modified coupling, because sample, doping and disorder systematics remain important; nevertheless, Nb, optimally doped YBCO and Ba(Fe,Co)$_2$As$_2$ show the suggestive trend $\lambda_{\rm opt}>\lambda_{\rm mag}$, whereas MgB$_2$ is consistent with the standard result $\lambda_{\rm opt}\simeq\lambda_{\rm mag}$ and Pb is not a clean test because of strong nonlocal corrections.