Tuning the electronic states to understand the interplay between superconductivity and topological states is crucial for realizing topological quantum computation. High pressure provides a unique avenue for tuning both superconducting and topological states. Here, we report the pressure tuning of superconductivity and topological band structures in ${\mathrm{Sn}}_4{\mathrm{P}}_3$. At ambient pressure, The Shubnikov–de Haas oscillations with nonzero Berry phases have been observed, and low-temperature angle-resolved photoemission spectroscopy measurements reveal nontrivial bands across the Fermi level, suggesting the topological character of ${\mathrm{Sn}}_4{\mathrm{P}}_3$. More intriguingly, upon applying pressure, two superconducting domes emerge with a maximum $T_c$ of 3.5 and 8.1 K at 5.6 and 42.1 GPa, respectively. High-pressure synchrotron X-Ray diffraction measurements combined with first-principles calculations show that the first dome is associated with a topological transition from topological insulator to topological semimetal, while the second dome is associated with a structural transition form the $R\overline{3}m$ phase to the $I4$/mmm phase. Our results suggest that ${\mathrm{Sn}}_4{\mathrm{P}}_3$ is a promising candidate as a topological superconductor and a platform for studying the interplay between superconductivity and band topology.

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• Pressure effects
• Superconducting phase transition
• Topological materials
• Topological superconductors