The study of quantum phase transitions in two-dimensional materials has garnered significant interest due to their potential applications in electronics and quantum computing. This research aims to investigate the quantum phase transitions in recently synthesized chalcogenide compounds. Using a combination of density functional theory and Monte Carlo simulations, we analyze the electronic properties and phase behavior of these two-dimensional systems under varying temperature and pressure conditions. The findings reveal a distinct transition point at which the material exhibits a shift from a topological insulator to a superconducting state. This transition is evidenced by marked changes in electronic band structure and conductivity characteristics. The study provides a comprehensive understanding of the critical phenomena associated with quantum phase transitions in these compounds, contributing to the broader field of condensed matter physics. Our results suggest avenues for tuning material properties through external parameters, offering potential pathways for the development of next-generation electronic devices. In conclusion, the research establishes a foundational understanding of the behavior of chalcogenide compounds under extreme conditions, framing future exploration within the realm of quantum materials.