Theory of pseudospin resonance for multiband superconductors

We formulate a generalized pseudospin formalism for multiband superconductors in the presence of an external perturbing electromagnetic field. Our theory naturally captures the effects of quantum band geometric quantities and is valid even for flat-band superconductors. As an interesting consequence of our theory, we show that there is an interband pairing fluctuations induced by the external field and mediated by the quantum band geometry. Surprisingly, this interband fluctuation is independent of the band gap, which can be understood from the geometric nature of such novel fluctuations. We derive the generalized equation of motion for the multiband pseudospin and the self-consistency equation. We present a formal solution to the pseudospin equation of motion in powers of the perturbing electromagnetic field. As a simple illustration of our theory, we calculate the Leggett modes for the two-band case.