Low-Energy Excitations in the Quantum Spin-Liquid $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_{3}$

The electrodynamic response of the organic spin-liquid candidate $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ has been measured in an extremely wide energy range ($10^{-13}$ to 2 eV) as a function of temperature (5 to 300 K). Below the Mott gap, excitations from the un-gapped spinon continuum cause a considerable contribution to the infrared conductivity, as suggested by the U(1) gauge theory. At THz frequencies we can identify a power-law behavior $\sigma(\omega) \propto \omega^{\beta}$ with two distinct exponents $\beta$ that change from 0.9 to 1.3 at low temperatures. The corresponding crossover scales with temperature: $\hbar\omega_c \approx k_B T$. The observed exponents differ by more than a factor of 2 from the theoretically predicted ones. The findings are compared with those obtained on Herbertsmithites.