  Nb$_3$Cl$_8$, a cluster Mott insulator with a distinctive magnetic molecular
orbital structure organized into a breathing kagome lattice, showcases critical
phase transitions under specialized conditions. By transitioning from
paramagnetic to nonmagnetic states below 90 K, we clarified this behavior
through combined nuclear magnetic resonance and low-temperature X-ray
diffraction studies, pointing to charge disproportionation as the driving
force. Subsequent investigations via angle-resolved photoemission spectroscopy
and first-principles calculations have disclosed topologically flat bands,
confirming advanced electronic characteristics in Nb$_3$Cl$_8$. These
discoveries not only deepen our comprehension of Mott insulators but also
broaden our grasp of the dynamic interrelations among topology, electron
interactions, and quantum phenomena in two-dimensional systems. The research on
Nb$_3$Cl$_8$ thus lays foundational knowledge for advancing the exploration of
quantum states in complex material systems, marking it as a critical model in
the ongoing evolution of condensed matter physics.
