Brynhildr in the Darkness

As a young boy, Murakami had a close friendship with a girl he nicknamed Kuroneko. Tragically, during an attempt to demonstrate the reality of extraterrestrial life to Murakami, she perished in an accident that he narrowly escaped. Burdened by guilt over his involvement, Murakami commits himself to the quest of proving aliens are real. Years later, a new student with enigmatic abilities joins his class, bearing a striking resemblance to Kuroneko and going by the name Kuroha, Neko.