Electronic Raman scattering of two-band superconductors: a time-dependent Landau-Ginzburg theory approach.

Electronic Raman scattering of two-band superconductors is studied based on the time-dependent Landau-Ginzburg theory. The focus is on the possible features of the π phase shift between the two superconducting order parameters which may be realized in the Fe-pnictides. The Raman response was computed up to the Gaussian fluctuations in the functional integral formalism including the long range Coulomb interaction with the four channels of symmetric and antisymmetric combinations of the phases and amplitudes of the two order parameters. The Raman spectra is found to be composed of the quasiparticle and the phase collective mode contributions without mixing between them. The contributions from the quasiparticle and the symmetric phase collective mode (the Anderson-Bogolyubov mode) are similar to the two-band superconductors without the π phase shift. The antisymmetric phase mode (the Leggett mode) originates from the fluctuations of the relative phase of the two order parameters. It lies between twice the smaller gap and twice the larger gap and is damped by the quasiparticles. However, this mode is eliminated by the long range Coulomb interaction in the zero-wavenumber limit.