Ultralow-Temperature Heat Transport Evidence for Residual Density of States in the Superconducting State of CsV₃Sb₅

V-based kagome superconductors AV_3Sb_5 (A = K, Rb, and Cs) host a charge density wave (CDW) and a topological nontrivial band structure, thereby providing a great platform to study the interplay of superconductivity (SC), CDW, frustration, and topology. Here, we report ultralow-temperature thermal conductivity measurements of CsV_3Sb_5 and Ta-doped Cs(V_0.86Ta_0.14)_3Sb_5 and scanning tunneling microscopy (STM) measurements of CsV_3Sb_5. The finite residual linear term of thermal conductivity at zero magnetic field suggests the existence of a residual density of states (DOS) in the superconducting state of CsV_3Sb_5. This is supported by the observation of non-zero conductance at zero bias in STM spectrum at an electronic temperature of 90 mK. However, in Cs(V_0.86Ta_0.14)_3Sb_5, which does not have CDW order, there is no evidence for the residual DOS. These results show the importance of CDW order for the residual DOS, and that a nodal s-wave gap or residual Fermi arc may be the origin of the residual DOS in such an unusual multiband kagome superconductor, CsV_3Sb_5.