Nodeless superconductivity in 4H$_{b}$-TaS$_{2}$ with broken time reversal symmetry

The transition metal dichalcogenide 4H$_{b}$-TaS$_{2}$ exhibits characteristics of topological edge modes and two-component superconductivity with time-reversal symmetry breaking (TRSB). The nature of the superconducting order parameter is a crucial issue that requires experimental investigation. Here, we report measurements of the magnetic penetration depth using a tunnel-diode-oscillator based technique, as well as the specific heat. Both the specific heat and the change in magnetic penetration depth ($\Delta$$\lambda$(T)) display an exponentially-activated temperature dependence, providing evidence for nodeless superconductivity in 4H$_{b}$-TaS$_{2}$. Moreover, the deduced superfluid density can be well described by a two-gap $s$-wave model, and such multigap superconductivity is consistent with there being multiple bands crossing the Fermi energy. These results constrain the possible pairing symmetries of 4H$_{b}$-TaS$_{2}$.