Rent Rahxephon (2002 - 2002)

Rahxephon is a Japanese anime series set in Japan at the end of 2012 when a floating city appears above Tokyo and a mysterious invader known as the Mu begin infiltrating society; the invasion culminates in a Nuclear war during which, in order to preserve control over the city, the Mu place a huge spherical barrier around Tokyo creating Tokyo Jupiter, a city in which humans are controlled by the Mu and attacked by the minions of the Mu, massive machines known as Dolems. Ordinary schoolboy Ayato finds himself caught up in the battle against the Dolem when a mysterious woman takes him to the secret resting place of the RahXephon, the only beings with the power to defeat the Dolem.