What is the expiation for someone who led the Dhuhr prayer while not in a state of ritual purity (wudu'), and is he required to repeat the prayer on behalf of the congregants, or is another expiation due, such as fasting or charity?

You committed a grave sin by intentionally praying without ablution, and you must repeat those prayers. The prayers of those who prayed behind you are valid, and they are not required to repeat them. You must offer sincere repentance, express remorse, and resolve not to return to such a sin. May Allah forgive you. There is no specific expiation required of you, but increasing good deeds is commendable.