$\mu$SR study of noncentrosymmetric superconductor PbTaSe$_2$

We present muon spin rotation ($\mu$SR) measurements on the noncentrosymmetric superconductor PbTaSe$_2$. From measurements in an applied transverse field between $H_{c1}$ and $H_{c2}$, we extract the superfluid density as a function of temperature in the vortex state. This data can be fit with a fully gapped two-band model, consistent with previous evidence from ARPES, thermal conductivity, and resistivity. Furthermore, zero field measurements show no evidence for a time reversal symmetry breaking field greater than 0.05~G in the superconducting state. This makes exotic fully gapped spin-triplet states unlikely, and hence we contend that PbTaSe$_2$ is characterized by conventional BCS s-wave superconductivity in multiple bands.