Symmetry-controlled multi-gap superconductivity and higher-order topological phases of MoTe₂

The transition-metal dichalcogenide MoTe₂ has been proposed as an ideal platform to intertwine superconductivity with band topology, yet a key experiment-tracking how its properties evolve across a pressure-tuned structural and topological phase transition-has remained elusive. Here, we map the superconducting landscape across these high-pressure regimes from the noncentrosymmetric type-II Weyl semimetal T_d phase to the centrosymmetric $1T^{\text{'}}$ phase using surface-sensitive soft point-contact Andreev spectroscopy combined with quantitative theoretical analysis. In the T_d phase, our spectra consistently reveal two distinct superconducting gaps that remain resolvable under an external magnetic field, implying robust and pressure-independent multi-gap superconductivity consistent with muon-spin-rotation evidence for two s-wave gaps at ambient pressure. In the $1T^{\text{'}}$ phase, reached by pressure along a topological pathway that connects the Weyl to the higher-order topological phase, we observe an s + p-wave surface response whose p-wave component follows the s-wave gap in temperature and is rapidly suppressed by a magnetic field-fingerprints of proximity-induced p-wave pairing between a bulk s-wave superconducting band and second-order topological surface states. This phenomenology aligns with theoretical analysis showing that the T_d phase hosts type-II Weyl points, whereas the $1T^{\text{'}}$ phase realizes a higher-order topological insulator arising from double-band inversion. Finally, we further propose that the resulting higher-order hinge boundary channels provide a natural route toward potential zero-energy Majorana corner modes under the observed s + p-wave proximity pairing, suggesting MoTe₂ as an intrinsic, pressure-tunable platform for multi-gap and s + p-wave topological superconductivity.