We revisited the high-pressure phase diagram of superconductor β-ThRhGe by measuring electrical resistivity and ac magnetic susceptibility under hydrostatic pressures. In addition to the low-pressure superconducting phase (SC1), our results revealed the emergence of another high-$T_{\mathrm{c}}$ superconducting phase (SC2) at pressures above 1 GPa, which coexists with SC1 and enhances with pressure along with the collapse of orthogonal-monoclinic structural transition near $\sim 3$ GPa. The superconducting transition temperature $\left(T_{\mathrm{c}}\right)$ of SC1 increases linearly with a pressure coefficient $\mathrm{d}{T}_{\mathrm{c}}/\mathrm{d}P\approx 0.69$ K/GPa, but the SC2 exhibits a dome-shaped pressure dependence, reaching a maximum value of $\sim 9.3$ K around 6.3 GPa, which is the highest for the reported ternary equiatomic intermetallic compounds. Our results suggest that SC1 and SC2 have significantly different superconducting coupling strengths and effective electron masses, further demonstrating two distinct superconducting states. The analysis of normal-state properties suggests that the enhanced $T_{\mathrm{c}}$ may be related to phonon softening accompanying structural transitions, and/or quantum fluctuations caused by possible structural instability. The evolution of $T_{\mathrm{c}}$ as a function of pressure and the physical mechanism of superconducting states were discussed on comparison to the previous reports in $\beta \text{−}\mathrm{ThR}{\mathrm{h}}_{1-x}{\mathrm{Ir}}_x\mathrm{Ge}$.

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• Electrical properties
• High-pressure studies
• Magnetic susceptibility
• Pressure effects
• Structural phase transition
• Superconductivity
• Pressure techniques
• Resistivity measurements