Question

Precisely speaking, does photon become massive or the phonon become massive, due to Higgs mechanism in superconductor?

Answer 1

Consider the low-energy field theories of superfluids and superconductors.  In superfluids, the spontaneous breaking of the order parameter's phase creates phonons as the massless Goldstone bosons.(Is it true? Or the massless excitation is the second sound rather than phonons.)  In superconductors, the spontaneous breaking of the charged order parameter's phase doesn't lead to a massless Goldstone boson. Due to the Higgs mechanism, it creates a massive Higgs mode instead.  Why saying the photons in a superconductor become massive due to the Higgs mechanism, instead of saying that the phonons, which ought to be created if the field is not charged, become massive due to Higss mechanism

Answer 2

Superfluid spontaneously breaks U(1)U(1) particle number conservation, and has nothing to do with the spatial translation symmetry. The Goldstone mode is called phonon because it is related to density fluctuations, but should not be confused with phonons in a crystal resulting from translation symmetry breaking.