%0 Journal Article %T Unusual persistence of superconductivity against high magnetic fields in the strongly-correlated iron-chalcogenide film FeTe:O$_{x}$ %A I. K. Dimitrov %A W. D. Si %A W. Ku %A S. -J. Han %A J. Jaroszynski %J Physics %D 2013 %I arXiv %R 10.1063/1.4818790 %X We report an unusual persistence of superconductivity against high magnetic fields in the iron chalcogenide film FeTe:O$_{x}$ below ~ 2.5 K. Instead of saturating like a mean-field behavior with a single order parameter, the measured low-temperature upper critical 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 strongly-correlated iron-based superconductors. %U http://arxiv.org/abs/1301.4487v3