Excitons and Plasmons in Superconductors
Abstract
The AndersonRickayzen equations of motion for a superconductor derived within the randomphase approximation (RPA) are used to investigate the collective excitations of superconductors. A spherical harmonic expansion is made of the twobody interaction potential V(k, k') and a spectrum of excitations whose energies lie within the energy gap 2∆ is obtained. These excitations may be characterized by the quantum numbers L and M involved in the potential expansion. For an Lstate exciton to exist, the Lwave part of the potential must be attractive at the Fermi surface. OddL excitons have unit spin and may be considered as spin waves. For sstate pairing in the superconducting ground state, the plasmon mode corresponds to the L=0 exciton whose energy is strongly modified by the longrange Coulomb interaction. For a general potential several bound states may exist for given L and M. If the Lwave potential is stronger than the swave part of the potential, the system is unstable with respect to formation of Lstate excitons. In this case, the ground state is formed with Lstate pairing, special cases of which are the pstate pairing considered by Fisher and the dstate pairing proposed recently by several authors for the ground state of He^{3} and nuclear matter. Corrections to the AndersonRickayzen equations are discussed which lead to a new set of exciton states if the Lwave potential is repulsive. These excitons are interpreted as bound electronhole pairs, as opposed to the particleparticle excitons present with an attractive Lwave potential.
 Publication:

Physical Review
 Pub Date:
 February 1961
 DOI:
 10.1103/PhysRev.121.1050
 Bibcode:
 1961PhRv..121.1050B