SPECTRAL PROPERTIES OF THE BOSON-FERMION MODEL IN THE SUPERCONDUCTINGSTATE

The spectral properties of a mixture of bosons hybridized with fermion pairs are studied in the superconducting state. Such a model exhibits two limiting behaviors. One is reminiscent of a BCS system, provided that the total concentration n of particles is below a certain critica l concentration n(c), in which case bosons exist only in thermally exc ited states. The other limit for n greater than or equal to n(c) descr ibes a situation largely controlled by the condensation of the bosons. The variation of the single-boson as well as collective excitations a s a function of n and for the entire temperature regime from T = 0 K t o T-c will be discussed, both with and without long-range Coulomb inte raction between the charge carriers. The method for calculation applie d here is based on the dielectric formalism and the use of Ward identi ties, currently used in the theory of the interacting Bose gas, which allows us to derive the density and current correlation functions cons istent with local charge-current conservation laws. In the absence of a Coulomb interaction the behavior of the system is characterized by t he existence of a sound-wave-like branch in the Bose single-particle a nd collective excitation spectrum. In the BCS regime the sound velocit y is proportional to the Fermi velocity while in the Bose regime it is proportional to the strength of the boson-fermion hybridization and d ecreases with the superfluid density as we approach T-c. In the presen ce of a long-range Coulomb interaction and in the Bose regime one obse rves, besides the usual optical plasmon mode at high frequency and cor responding to in-phase density oscillation of the two subsytems, an ou t-of-phase collective mode in the two particle continuum just above th e gap. Moreover, upon approaching T-c a relatively well-defined quasip article feature starts to emerge within the gap and is seen in both th e Bose single-particle excitation and the density oscillation spectrum . In the BCS regime, due to the very small number of occupied bosonic states, the low-energy quasiparticle features are absent.