We present the ultra-low-temperature thermal conductivity measurements on single crystals of the transition-metal dichalcogenide material $4{\mathrm{Hb}\text{−}\mathrm{TaS}}_2$, which has recently been proposed as a topological superconductor candidate. In zero field, a small residual linear term ${\kappa }_0/T$ is observed, indicating the existence of a residual density of states in the superconducting state. The slow field dependence of ${\kappa }_0/T$ at low fields rules out the presence of nodes in the superconducting gap, and the S-shaped field dependence across the full field range suggests multiple superconducting gaps in $4{\mathrm{Hb}\text{−}\mathrm{TaS}}_2$. Our results provide evidence for multiband gapless superconductivity in $4{\mathrm{Hb}\text{−}\mathrm{TaS}}_2$, and the residual density of states come from certain gapless Fermi surfaces.

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• Superconductivity
• Topological superconductors