Nodeless superconductivity in kagome metal CsV$_{3}$Sb$_{5}$ with and without time reversal symmetry breaking

The kagome metal CsV$_{3}$Sb$_{5}$ features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time-reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV$_{3}$Sb$_{5}$ emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional $s$-wave superconductivity. Moreover, our measurements of the self-field critical current ($I_{c,sf}$), which is related to the London penetration depth, also confirm conventional $s$-wave superconductivity with strong coupling. Finally, we measure $I_{c,sf}$ where the CDW order is removed by pressure and superconductivity emerges from the pristine normal state. Our results show that $s$-wave gap symmetry is retained, providing strong evidence for the presence of conventional $s$-wave superconductivity in CsV$_{3}$Sb$_{5}$ irrespective of the presence of the TRSB