Geometric Leggett mode in the two-band superconductors
We calculate the order parameter fluctuations in multiband superconductors to first order in external electromagnetic field. We show that there is an induced fluctuation that is purely mediated by the band geometry. We then consider the Bernevig-Hughes-Zhang model with mean-field pairing potential. We show that even if the initial pairing is purely in the lower band, there will be an interband pairing fluctuations induced by the external field and mediated by the band geometry. We calculate the Leggett mode between the order parameter of the lowest band and the induced interband pairing and show that this mode persists even for large band gap, which is consistent with the geometric nature of such mode. Furthermore, unlike the conventional Leggett mode, this geometric mode persists even in the flat band superconductors.