Fermi liquid theory on transport phenomena in the superconducting state

Transport phenomena in the superconducting state are discussed microscopically on the basis of Fermi liquid theory. In this paper we put an emphasis on many bod effects. The optical conductivity is shown to have the correction to a current vertex which is explicitly temperature dependent. This current vertex cannot be identified with the velocity of quasiparticles as in the normal state. From these arguments it is concluded that validity of applying results obtained in the normal state simply to the superconducting state is an issue to be carefully studied and not guaranteed in some cases. Several quantities basic in Fermi liquid theory (the renormalization factor, the velocity of quasiparticles and the relation which holds in Galilean invariant case) which have been assumed to hold and given as external parameters in previous works are derived by using Ward-Takahashi identities. These derivations justify the arguments: based on the Fermi liquid theory. The many body effect on magnetic field penetration depth is also discussed and an emphasis is put on the difference between this quantity and the superconducting carrier density. By putting together the results obtained for the electromagnetic response case, it is shown that the weight of coherent part which couples to the electromagnetic field is conserved from the normal state to the superconducting state. Thermal conductivity is derived microscopically and the current vertex is shown to be written by the energy current of Bogoliubov quasiparticles This fact is important for superconductors with anisotropic gaps.