Gapless superconductivity in Nb thin films probed by terahertz spectroscopy.

Time reversal symmetry (TRS) breaking often generates exotic quantum phases in condensed matter. In superconductors, TRS breaking by an external magnetic field not only suppresses superconductivity but also leads to a novel quantum state called the gapless superconducting state. Here we show that magneto-terahertz spectroscopy provides us with a rare opportunity to access and explore the gapless superconducting state of Nb thin films. We present the complete functional form of the superconducting order parameter for an arbitrary magnetic field, for which a fully self-consistent theory is, surprisingly, yet unavailable. We observe a Lifshitz topological phase transition with a vanishing quasiparticle gap everywhere on the Fermi surface, whereas the superconducting order parameter smoothly crosses over from the gapped to the gapless regime. Our observation of the magnetic pair-breaking effects in Nb challenges traditional perturbative theories and opens a pathway to further exploring and manipulating the exotic state of gapless superconductivity.