Abstract
The charge dynamics of spin-liquid states described by U(1) gauge theory coupling to fermionic spinons is discussed in this paper. We find that the gapless spinons give rise to a power-law optical conductivity inside the charge gap. The theory is applied to explain the unusual optical conductivity observed recently in the organic compound kappa-(BEDT-TTF)2Cu2(CN){3}. We also propose an optical experiment to search for the in-gap excitations in the kagome spin-liquid insulator.
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