The lower critical field $B_{c1}$ of a narrow superconducting thin-film strip sets the thermodynamic scale for vortex-free operation in a perpendicular magnetic field. The standard Pearl–London estimate requires a phenomenological vortex-core cutoff, because the London theory does not resolve the core. We formulate a microscopic theory for a dirty strip by solving the two-dimensional Usadel equations in the film plane, with the applied field included directly in the gauge-invariant momentum. Self-consistent vortex and Meissner solutions are computed at fixed field, and $B_{c1}$ is obtained from their Gibbs energy difference. The calculation resolves the vortex core and its finite-width deformation without introducing a cutoff. The resulting vortex self-energy is larger than the naive Pearl–London estimate and cannot, in general, be represented by a London logarithm with a single width-independent cutoff. The formulation applies at any $T<T_c$ and provides a microscopic basis for predicting $B_{c1}$ in superconducting nanostrips and related thin-film devices.

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• Mesoscopics
• Optoelectronics
• Vortices in superconductors
• Nanoribbon
• Superconducting devices
• Thin films
• Type-II superconductors
• Usadel equation