Monolayer ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ has been considered as the first large-gap Kane-Mele quantum spin Hall insulator and is therefore expected to exhibit distinctive topological phases and physical properties. Here, we use monolayer ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ as the work substance to demonstrate a quantum Stirling cycle driven by an external electric potential and an off-resonant light. Through theoretical analyses and numerical calculations, we find that monolayer ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$ is an excellent material to perform a quantum Stirling cycle, while on the other hand, the quantum Stirling cycle can be used to characterize the topological phase transitions (TPTs) in monolayer ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$. The results show that all four types of quantum thermal machine modes can be realized, including heat engine, refrigerator, Joule pump, and cold pump in the quantum sense. Moreover, it is easy to perform the transform among these operating modes by adjusting the electric potential, off-resonant light, and reservoir temperatures, illustrating the machine's high versatility. Furthermore, when operated as a quantum heat engine, the device achieves an efficiency that significantly exceeds that of Xene-based quantum Stirling engines. Most importantly, we demonstrate that across all four operational modes, the extrema in the work output provide clear signatures for detecting the TPTs in monolayer ${\mathrm{Pt}}_2{\mathrm{HgSe}}_3$. Additionally, in the heat engine mode, the TPTs can be detected at both low and high temperatures, in sharp contrast to graphenelike Xene monolayers such as stanene, where quantum Stirling engines fail to detect the TPTs at high temperatures.

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• Phase transitions
• Quantum thermodynamics
• Topological materials
• Two-dimensional electron system