Power-law conductivity inside the Mott gap: application to kappa-(BEDT-TTF)2Cu2(CN){3}.

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.