Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB2

In 1966, Leggett used a two-band superconductor to show that a new collective mode could exist at low temperatures, corresponding to a counterflow of the superconducting condensates in each band. Here, the theory of electronic Raman scattering in a superconductor by Klein and Dierker (1984) is extended to a multiband superconductor. Raman scattering creates particle/hole (p/h) pairs. In the relevant A(1g) symmetry, the attraction that produces pairing necessarily couples excitations of superconducting pairs to these p/h excitations. In the Appendix, it is shown that for zero wave-vector transfer q, this coupling modifies the Raman response and makes the long-range Coulomb correction null. The two-band result is applied to MgB2 where this coupling activates Leggett's collective mode. His simple limiting case is obtained when the interband attractive potential is decreased to a value well below that given by local-density approximation (LDA) theory. The peak from Leggett's mode is studied as the potential is increased through the theoretical value. With realistic MgB2 parameters, the peak broadens through decay into the continuum above the smaller (pi band) superconducting gap. Finite q effects are also taken into account, yielding a Raman peak that agrees well in energy with the experimental result by Blumberg et al. [Phys. Rev. Lett. 99, 227002 (2007)]. This approach is also applied to the q=0, two-band model of the Fe pnictides considered by Chubukov et al. [Phys. Rev. B 79, 220501 (R) (2009)]