Optical sum rule in multiband superconductors

In the standard Bardeen-Cooper-Schrieffer model, the optical sum rule establishes the relation between the superfluid density and the change in the integral of the real part of the conductivity over the frequency after the transition to the superconducting state. In conventional low-temperature superconductors, these two values become equal if the conductivity is integrated up to a frequency of the order of several widths of the superconducting gap. Optical experiments for high-T c cuprate superconductors performed by many research groups over the world demonstrate that the integration up to a much higher frequency (of the order of the band width) is needed to reproduce the spectral weight of the superfluid component. An interpretation of these experiments has been proposed with allowance for the complex crystal structure of cuprates, in which several orbitals of different symmetries approach the Fermi level.