Thermodynamics and heat transport of quantum spin liquid candidates NaYbS$_2$ and NaYbSe$_2$

We study the ultralow-temperature thermodynamics and thermal conductivity ($\kappa$) of the single-crystal rare-earth chalcogenides NaYbS$_2$ and NaYbSe$_2$, which have an ideal triangular lattice of the Yb$^{3+}$ ions and have been proposed to be quantum spin liquid candidates. The magnetic specific heat divided by temperature $C_{\rm{mag}}/T$ is nearly constant at $T <$ 200 mK, which is indeed the indication of the gapless magnetic excitations with a constant density of states. However, we observe a vanishingly small residual term $\kappa_0/T$, which points to the absence of mobile fermionic excitations in these materials. Both the weak temperature dependence of $\kappa$ and the strong magnetic-field dependence of $\kappa$ suggest the significant scattering between the spinons and phonons, which actually supports the existence of gapless or tiny-gapped quantum spin liquid. Moreover, the $\kappa(B)/\kappa(0)$ isotherms show a series of field-induced magnetic transitions for $B \parallel a$, confirming the easy-plane anisotropy, which is consistent with the results of ac magnetic susceptibility. We expect our results to inspire further interests in the understanding of the spinon-phonon coupling in the spin liquid systems.