A Certain Magical Index(2008)

Touma Kamijou is a student living in Academy City, a highly advanced place in terms of technology. Despite being gauged as a level zero esper (no powers), he possesses on his right hand the Imagine Breaker, an ability that negates any power whatsoever. Touma finds a young girl named Index who is trying to run away from Necessarius, a powerful magic organization that she is member of. Blessed with the skill of memorizing any sort of information, she holds 103,000 forbidden magical books within her head. As science and magic cross paths, Touma must face several dangers amid espers and magicians who appear in the exciting scientific town.