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Why does the real part of conductivity increase with increase in scattering rate at frequencies much larger than the scattering rate? I understand the mathematical implication, but do not understand it intuitively. At low frequencies, increasing scattering rate increases losses and the real part of conductivity decreases. Shouldn't higher scattering rates mean more loss (heat) and less conductivity? What additional effects come into play at frequencies much greater than the scattering rates that leads to increasing conductivity while increasing scattering rates?

P.S : I am asking in a more general sense that applies to all metals, however my above question is motivated by seeing the effects in graphene. The chemical potential is kept constant while the scattering rate is varied.

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