Unusual Persistence of Superconductivity Against High Magnetic Fields in the Strongly-Correlated Iron-Chalcogenide Film FeTe:O$_{x}$

We report an unusual persistence of superconductivity against high magnetic fields in the iron chalcogenide film FeTe:O$_{x}$ below 2.52 K. Instead of saturating like a mean-field behavior with a single order parameter, the measured low-temperature upper criticial field increases progressively, suggesting a large supply of superconducting states accessible via magnetic field or low-energy thermal fluctuations. We demonstrate that superconducting states of finite momenta can be realized within the conventional theory, despite its questionable applicability. Our findings reveal a fundamental characteristic of superconductivity and electronic structure in the iron-based superconductors.