What is the difference between Collective excitations and quasiparticle in superconductor? How to consider superconductors' optical response?

Question

In the BCS theory, superconductors can be seen as Cooper pair condensates and quasiparticle excitations (Bogoliubov quasiparticle). But in Ginzburg-Landau's theory of superconductivity phenomenology, combined with the language of QFT, there will be collective excitations: (1) phase fluctuations (Nambu-Goldstone mode), (2) amplitude fluctuations (Higgs mode).

So, is there an inclusive or intersecting relationship between the two languages? When we consider superconductors' photoconduction and optical response, how to ensure that there is no omission and no repetition?

Answer 1

It is not entirely clear what is meant by Ginzburg-Landau's theory of superconductivity phenomenology, combined with the language of QFT. Ginsburg-Landau is normally a mean field theory, so no quasiparticles there.

Collective excitations is a very general term: in principle, quasiparticles (in general) are collective excitations... although the term usually implies long-range bosonic modes, such as photons, magnons, etc. (rather than electrons/holes or excitons). However, Bogoliubov quasiparticles are a very specific type of excitations, so they do not encompass all the excitations possible in superconductor.

One could formally quantize Landau-Ginzburg theory (or Landau-Ginsburg equation), and thus obtain an effective low-energy theory. Excitations in such theory would be long-range in time and space, whereas Bogoliubov quasiparticles have well defined dispersion relation, and can be created in small quantities. Thus, we are dealing with two opposite limits of the same thing here. In a normal metal a similar relation exists between electrons (quasiparticles) and plasmons (collective excitations, which are also quasiparticles).