We show that while an orbital magnetic field and disorder, acting individually, weaken superconductivity, acting together they produce an intriguing evolution of a two-dimensional type-II $s$-wave superconductor. For weak disorder, the critical field $H_c$ at which the superfluid density collapses is coincident with the field at which the superconducting energy gap gets suppressed. However, with increasing disorder these two fields diverge from each other, creating a pseudogap region with insulating vortex cores. Our results naturally explain two outstanding puzzles: the gigantic magnetoresistance peak observed as a function of magnetic field in thin disordered superconducting films and the disappearance of the celebrated zero-bias Caroli–de Gennes–Matricon peak in the local density of states at the vortex core in disordered superconductors.

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• Impurities in superconductors
• Magnetoresistance
• Pseudogap
• Superconducting fluctuations
• Superconducting phase transition
• Superconductor-insulator transition
• Vortices in superconductors
• Disordered systems
• Thin films
• Methods in superconductivity