Terahertz spectroscopy of Nb thin films in the gapless superconducting state

By using magneto-terahertz spectroscopy, we explore the gapless superconducting state of Nb thin films. We report the detailed evolutions of the pair-breaking parameter, the spectroscopic gap, the superconducting order parameter, and the London penetration depth over the entire range of in-plane magnetic fields up to the upper critical field of 3.5 T, including the gapless regime where the gap itself is zero but the order parameter is still finite. The complete functional form of the order parameter has been found for an arbitrary magnetic field, for which a fully self-consistent theory is, surprisingly, yet unavailable. While the spectroscopic gap collapses as Nb enters the gapless regime, the superconducting order parameter decreases smoothly until it vanishes at the upper critical field. The gapless regime reveals a non-parabolic field dependence of the pair-breaking parameter and an extreme nonlinear Meissner effect, previously unseen in low-field measurements carried out in the gapped superconducting state. Our results for the magnetic pair-breaking effects in Nb challenge traditional perturbative theories in several key aspects.