Power-law conductivity inside the mott gap: Application to κ-(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 κ-(BEDT-TTF)2Cu2(CN)3. We also propose an optical experiment to search for the in-gap excitations in the kagome spin-liquid insulator.