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We present the ultra-low-temperature thermal conductivity measurements onsingle crystals of the prototypical charge-density-wave material 1$T$-TaS$_2$,which was recently argued to be a candidate for quantum spin liquid. Ourexperiments show that the residual linear term of thermal conductivity at zerofield is essentially zero, within the experimental accuracy. Furthermore, thethermal conductivity is found to be insensitive to the magnetic field up to 9T. These results clearly demonstrate the absence of itinerant magneticexcitations with fermionic statistics in bulk 1$T$-TaS$_2$ and, thus, put astrong constraint on the theories of the ground state of this material.

Heat transport study of the spin liquid candidate 1T-TaS2