Collective excitations and response functions of two-band band-singlet and spin-tripletsuperconductors

Abstract

The two-band band-singlet and spin-triplet superconductors are studied in the frameworkof functional integrals with a focus on collective excitations and their influences on responsefunctions. The long range Coulomb interaction has been included to preserve the electromagneticU(1) gaugeinvariance. The U(1) phase fluctuation and the spin wave are identified as the collective excitations.The longitudinal spin response function turns out to be solely determined byquasiparticle excitation. The transverse spin response function is determinedby both the quasiparticle excitation and the spin wave. The spin wave is foundnot to be renormalized by long range Coulomb interaction. The densityresponse function is determined by both the quasiparticle excitation and theU(1) phase fluctuation, but in contrast to the case of spin response functions, both of them arestrongly renormalized by the long range Coulomb interaction. The nondegeneracy of theband energy can affect the response functions significantly through the contribution bycollective excitations.