Thermal conductivity of the quantum spin liquid candidate herbertsmithite

Hosting a S = 1/2 system on a kagome lattice, herbertsmithite (ZnCu₃(OH)₆Cl₂) is a leading candidate in the search for quantum spin liquids. Despite the absence of magnetic ordering down to very low temperature and several probes detecting a significant density of low-energy states, a debate persists on whether this material has gapless spinon excitations. Our thermal conductivity measurements down to 60 mK show no signs of the T-linear contribution to heat conduction that is expected from mobile spinons. Instead, our results suggest that the low-energy spin excitations in herbertsmithite are either localized or gapped.