The experimental realization of a quantum spin liquid has been long sought after. While a handful of candidate materials exist, including the triangular organic ?-(BEDT-TTF)2Cu2(CN)3 and the kagome ZnCu3(OH)6Cl2 (Herbertsmithite), the precise nature of their ground states is still elusive. Recent theory has predicted a contribution to the low frequency optical conductivity by a gapless spin liquid state with an internal gauge field. In particular, a power-law dependence on frequency with exponent not much larger than 1 is expected within the Mott gap. Here we present the optical conductivity of a large single crystal sample of Herbertsmithite, measured using terahertz time-domain spectroscopy. We observe a power law contribution to the conductivity within the kagome planes with exponent 1.4, which is absent in the out-of-plane conductivity. Our results provide evidence of a gapless spin liquid state in Herbertsmithite, and demonstrate the importance of gauge fields in its low energy excitations.
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