Evidence for Multiband Gapless Superconductivity in the Topological Superconductor Candidate 4Hb-TaS_{2}

We present the ultra-low-temperature thermal conductivity measurements on single crystals of the 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 κ_{0}/T is observed, indicating the existence of a residual density of states in the superconducting state. The slow field dependence of κ_{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.