Quasiparticle Interactions in Two and Three Dimensional Superconductors

I investigate the difference between the quasiparticle properties in two dimensional(2D)and three dimensional(3D) s-wave superconductors. Using the original BCS model for the pairing interaction and direct Coulomb interaction I show that quasiparticle interactions lead to a stronger energy dependence in the single-particle self-energies in 2D than in 3D superconductors. This difference arises from the presence of the low lying collective mode of the order parameter in the 2D case which ensures that oscillator strength in the response function is at low frequencies, $\sim \Delta$. This strong quantitative difference between 2D and 3D superconductors points to the importance of treating quasiparticle interactions in low dimensional superconductors rather than assuming that renormalizations remain unchanged from the normal state.