Kizuna Hida can activate a Heart Hybrid Gear, the same armor every student pilots against otherworldly invaders at Ataraxia, an academy built on a city that floats out at sea, but his output is too weak to matter until his older sister, who commands the place, has him transferred in anyway. There, ace pilot Aine Chidorigafuchi and her squad discover that Kizuna's power actually flows the other way: physical contact with him is what recharges their gear mid-battle. His new life is built around that reluctant fact as much as around the war.