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Theories and experiments on dirty superconductors are sophisticated butimportant for both fundamentals and applications. It becomes more challengingwhen magnetic fields are present, because the field distribution, the electrondensity of states, and the superconducting pairing potentials are nonuniform.Here we present tunneling microspectroscopic experiments on NbC single crystalsand show that NbC is a homogeneous dirty superconductor. When applying magneticfields to the sample, we observe that the zero-energy local density of statesand the pairing energy gap follow an explicit scale relation proposed by deGennes for homogeneous dirty superconductors in high magnetic fields.Surprisingly, our experimental findings suggest that the validity of the scalerelation extends to magnetic field strengths far below the upper critical fieldand call for new nonperturbative understanding of this fundamental property indirty superconductors. On the practical side, we use the observed scalerelation to drive a simple and straightforward experimental scheme forextracting the superconducting coherence length of a dirty superconductor inmagnetic fields.

Direct Observation of the Scale Relation between Density of States and Pairing Gap in a Dirty Superconductor