Tokyo ESP Season 1 (2014)

Rinka Urushiba is a normal high school girl, until she encounters a penguin and shoals of glowing fish swimming through the sky. She looses consciousness only to awaken with the power to move through inanimate objects. At first she thought it was a hallucination if it were not for Kyotaro Azuma who witnessed the event and who, incidentally, has the ability to teleport. They decide to use their powers to combat people who might use their powers for evil.