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We study the critical temperature of a superconductive material in a weakexternal electric potential via a linear approximation of the BCS functional.We reproduce a similar result as in [Frank, Hainzl, Seiringer, Solovej, 2016]using the strategy introduced in [Frank, Hainzl, Langmann, 2018], where weconsidered the case of an external constant magnetic field.

The BCS critical temperature in a weak external electric field via a linear two-body operator