Recently superconductivity was discovered in the Kagome metal AV3Sb5 (A = K, Rb, and Cs), which has an ideal Kagome lattice of vanadium. These V-based superconductors also host charge density wave (CDW) and topological nontrivial band structure. Here we report the ultralow-temperature thermal conductivity and high pressure resistance measurements on CsV3Sb5 with Tc = 2.5 K, the highest among AV3Sb5. A finite residual linear term of thermal conductivity at zero magnetic field and its rapid increase in fields suggest nodal superconductivity. By applying pressure, the Tc of CsV3Sb5 increases first, then decreases to lower than 0.3 K at 11.4 GPa, showing a clear first superconducting dome peaked around 0.8 GPa. Above 11.4 GPa, superconductivity re-emerges, suggesting a second superconducting dome. Both nodal superconductivity and superconducting domes point to unconventional superconductivity in this V-based superconductor. While our finding of nodal superconductivity puts a strong constrain on the pairing state of the first dome, which should be related to the CDW instability, the superconductivity of the second dome may present another exotic pairing state in this ideal Kagome lattice of vanadium.
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