We investigated the effect of hydrostatic pressure on the quasi-one-dimensional superconductor ${\mathrm{TaSe}}_3$, using Raman spectroscopy, synchrotron x-ray diffraction, and first-principles calculations. Our studies reveal the weak topological nature of ${\mathrm{TaSe}}_3$ under ambient conditions. The application of hydrostatic pressure to the material shows a series of topological quantum phase transitions. Specifically, we observe a transition from weak to strong topological phase at 3 GPa followed by another transition to a weak topological phase at 8 GPa. The topologically dark surfaces in the initial and final weak topological phases are different, as indicated by the weak indices (101) and (100), respectively. The surface spectrum of ${\mathrm{TaSe}}_3$ in the strong phase indicates a Dirac point at the center of the Brillouin zone with spin helicity. We also observe the existence of Rashba-like spin splitting of the electronic states on the surfaces, owing to the discontinuous nature of the potential at the surface and the presence of spin-orbit coupling. Our study reveals the extremely rich properties that emerge in ${\mathrm{TaSe}}_3$ with the application of pressure, shedding light on its importance in next-generation quantum devices.

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• High-pressure studies
• Topological insulators
• Crystal structures
• Crystallography
• Density functional theory
• Electronic structure
• Raman spectroscopy