Reentrant Transition in Thin-Film Superconductors of TiN under Spin Paramagnetic Limitation

A reentrant transition with respect to temperature is observed for superconducting thin films of TiN ranging in thickness from ∼4 to ∼10 nm under high magnetic fields applied parallel to the film plane. A first-order transition follows the reentrant transition at low temperatures for some of these films. These results are similar to those observed in thin Al films and indicate the existence of a high-entropy superconducting state which was predicted for a gapless superconductor under spin paramagnetic limitation.