Tokyo ESP

Tokyo ESP (東京ESP, Tōkyō Īēsupī) is a manga written and illustrated by Hajime Segawa. It was serialized in Shounen Ace from February 26, 2010 to July 26, 2016. An anime adaptation aired from July 12, 2014 to September 27, 2014.

Plot
Tokyo ESP begins with Rinka Urushiba as a fairly normal high school girl, though she is a bit poor and her only family is her father. This forces her to work as a waitress after high school to raise money for them to secure rent and food. One day, she sees a penguin and some glowing fish swimming through the sky. Rinka might have thought it was a hallucination if there had not been another witness with her, a boy from her school with a strangely scratched-up face. Contact with a fish causes her to pass out, and when she awakens, she has developed the power to move through inanimate objects such as the floor of her apartment. She meets a fellow high school student named Kyotaro Azuma, who has the ability to teleport. The two of them use their ESP powers to take on individuals who have decided to use them for evil. However, there is an organization that plans for a bigger scheme to secure utopia with their ranks consisting of strong ESP fighters and users.

Official

 * Official anime website (Japanese)