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 ${\text{MgB}}_2$ 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 ${\text{MgB}}_2$ 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)].

• Received 13 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.014507