The authority you are looking for is District of Columbia v. Heller, 554 U.S. 570 (2008).
In this judgement, SCOTUS explained limitations of the second amendment. There is extensive historical analysis, but for your purpose, this is the important clause:
[T]he right to keep arms involves, necessarily, the right to use such arms for all the ordinary purposes, and in all the ordinary modes usual in the country, and to which arms are adapted, limited by the duties of a good citizen in times of peace.
To put it short: Since nuclear weapons are unlikely to be useful for ordinary purpose usual in the US by a good citizen in times of peace, they are not covered by the second amendment.