Evidence for multiband gapless superconductivity in the topological superconductor candidate 4Hb-TaS2

We present the ultralow-temperature thermal conductivity measurements on single crystals of transition-metal dichalcogenide material 4Hb-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 4Hb-TaS$_{2}$. Our results provide evidence for multiband gapless superconductivity in 4Hb-TaS$_{2}$, and the residual density of states come from certain gapless Fermi surfaces.