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EtMe$_3$Sb[Pd(dmit)$_2$]$_2$, an organic Mott insulator with nearly isotropictriangular lattice, is a candidate material for a quantum spin liquid, in whichthe zero-point fluctuations do not allow the spins to order. The itinerantgapless excitations inferred from the thermal transport measurements in thissystem have been a hotly debated issue recently. While the presence of a finitelinear residual thermal conductivity, $\kappa_0/T \equiv \kappa/T (T\rightarrow 0)$, has been shown [M. Yamashita {\it et al.} Science {\bf 328},1246 (2010)], recent experiments [P. Bourgeois-Hope {\it et al.}, Phys. Rev. X{\bf 9}, 041051 (2019); J. M. Ni {\it et al.}, Phys. Rev. Lett. {\bf 123},247204 (2019)] have reported the absence of $\kappa_0/T$. Here we show that thelow-temperature thermal conductivity strongly depends on the cooling process ofthe sample. When cooling down very slowly, a sizable $\kappa_0/T$ is observed.In contrast, when cooling down rapidly, $\kappa_0/T$ vanishes and, in addition,the phonon thermal conductivity is strongly suppressed. These results suggestthat possible random scatterers introduced during the cooling process areresponsible for the apparent discrepancy of the thermal conductivity data inthis organic system. The present results provide evidence that the true groundstate of EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ is likely to be a quantum spin liquidwith itinerant gapless excitations.

Presence and absence of itinerant gapless excitations in the quantum spin liquid candidate EtMe$_3$Sb[Pd(dmit)$_2$]$_2$