  A notable characteristic of PbTaSe$_2$, a prototypical noncentrosymmetric
(NCS) superconductor, is that its superconductivity can be modulated through a
structural transition under hydrostatic pressure [Phys. Rev. B 95, 224508
(2017)]. Here we report on simultaneous pressure-sensitive point-contact
Andreev reflection (PCAR) spectroscopy and bulk resistance measurements on
PbTaSe$_2$, to elucidate the nature of the surface and bulk superconductivity
and their evolution with hydrostatic pressure. It is found that in high
pressure region the superconducting gap opening temperature $T_c^A$ is
significantly lower that the bulk resistive transition temperature $T_c^R$,
revealing a clear experimental signature of surface-bulk separation associated
with enhanced antisymmetric spin-orbit coupling (ASOC). The PCAR spectra,
reflecting the superconducting surface state, are analyzed with the
Blonder-Tinkham-Klapwijk theory, yielding an isotropic $s$-wave full BCS-gap in
the strong coupling regime. Analysis based on a modified McMillan formula
indicates a sizable coupling strength contributed from ASOC for the
superconducting surface state. These results suggest the coexistence of full
gap $s$-wave superconductivity and topological surface states in PbTaSe$_2$,
indicating that this NSC with significantly enhanced ASOC may offer a solid
platform to investigate the topological aspect in the superconducting
condensate.
