Superconductivity (SC) remains a captivating field of research, promising transformative applications in energy, computing, and quantum technologies. Despite decades of investigation, the mechanisms underlying unconventional SC are not yet fully understood, motivating the discovery and study of new materials with exotic properties. The noncentrosymmetric superconductor ${\mathrm{PbTaSe}}_2$ offers a compelling platform to explore unconventional SC, where the absence of inversion symmetry can give rise to mixed-parity pairing states and novel superconducting phenomena. In this work, we investigate its superconducting properties through combination of specific-heat and muon spin relaxation ($\mu \mathrm{SR}$) measurements, with the latter performed under both ambient and applied hydrostatic pressure. At ambient pressure, ${\mathrm{PbTaSe}}_2$ exhibits a superconducting transition at ${\mathit{T}}_c=3.6\mathrm{K}$, with a normalized heat capacity jump $\mathrm{\Delta }C/\gamma {\mathit{T}}_c=1.4$, indicating weak electron-phonon coupling. A combined analysis of specific-heat and $\mu \mathrm{SR}$ data under ambient pressure reveals the presence of multigap $s+s$-wave superconductivity, characterized by two distinct superconducting gaps. Upon the application of hydrostatic pressure up to 3 kbar, ${\mathit{T}}_c$ is significantly suppressed from 3.6 K to approximately 2.5 K, likely due to structural modifications involving the shift of the Pb atomic position without any change in the overall crystal symmetry. Notably, the multigap nature of the superconducting state persists under applied pressure. Furthermore, zero-field $\mu \mathrm{SR}$ measurements confirm the absence of spontaneous internal magnetic fields at ambient as well as applied pressure, demonstrating that time-reversal symmetry remains intact in the superconducting state despite the noncentrosymmetric crystal structure of ${\mathrm{PbTaSe}}_2$. Overall, these findings establish ${\mathrm{PbTaSe}}_2$ as a promising platform to study the unconventional SC and the interplay between multigap behavior, topology, and electron-phonon coupling under pressure.

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• Density of states
• Fermi surface
• Multiband superconductivity
• Spin-orbit coupling
• Superconducting gap
• Superconductivity
• Topological superconductors