Excitons and Plasmons in Superconductors

The Anderson-Rickayzen equations of motion for a superconductor derived within the random-phase approximation are used to investigate the collective excitations of superconductors. A spherical harmonic expansion was made of the two-body interaction potential V(k,k') and a spectrum of excitations with energies lying within the energy gap 2 delta was obtained. These excitations may be characterized by the quantum numbers L and M involved in the potential expansion. For an L-state exciton to exist, the L-wave part of the potential must be attractive at the Fermi surface. OddL excitons have unit spin and may be considered as spin waves. For s-state pairing in the superconducting ground state, the plasmon mode corresponds to the L = 0 exciton. the energy of which is strongly modified by the long-range Couiomb interaction. For a general potential several bound states may exist for given L and M. If the L-wave potential is stronger than the s-wave part of the potential. the system is unstable with respect to formation of L-state excitons. In this case, the ground state is formed with Lstate pairing. Corrections to the Anderson-Rickayzen equations are discussed which lead to a new set of exciton states if the L-wave potential is repulsive. Thesemore » excitons are interpreted as bound electron-hole pairs, as opposed to the particle-particle excitons present with an attractive L-wave potential. (auth)« less