Quantum spin liquids attract great interest due to their exceptional magnetic properties characterized by the absence of long-range order down to low temperatures despite the strong magnetic interaction. Commonly, these compounds are strongly correlated electron systems, and their electrodynamic response is governed by the Mott gap in the excitation spectrum. Here we summarize and discuss the optical properties of several two-dimensional quantum spin liquid candidates. First we consider the inorganic material Herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$ and related compounds, which crystallize in a kagome lattice. Then we turn to the organic compounds $beta^{prime}$-EtMe$_3$-Sb-[Pd(dmit)$_2$]$_2$, $kappa$-(BEDT-TTF)$_2$Ag$_2$(CN)$_3$ and $kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, where the spins are arranged in an almost perfect triangular lattice, leading to strong frustration. Due to differences in bandwidth, the effective correlation strength varies over a wide range, leading to a rather distinct behavior as far as the electrodynamic properties are concerned. We discuss the spinon contributions to the optical conductivity in comparison to metallic quantum fluctuations in the vicinity of the Mott transition.
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