Electric charge amplitude mode superconductivity

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Hello,

I have a question about the Higgs mode in superconductivity. In this doc, it is said, page 12, that the Higgs mode has no electric charge. But it couples nonlinearly with the photon (in the Ginzburg-Landau theory there is a term A²h with A the vector potential and h the Higgs mode). So I don't understand this apparent contradiction.

Thanks.
 

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