Structure factor and quantum weight of twisted bilayer semiconductors at fractional fillings

The structure factor is an essential observable for probing crystal structures and charge density correlations in real materials, recently gaining prominence as a tool in analytical and numerical studies of topological quantum matter. Here we employ the static structure factor to explore the phase diagram of twisted transition metal dichalcogenides (TMDs), specifically tMoTe2, at a filling factor n=2/3 under varying displacement fields using band-projected exact diagonalization (BPED). Our results reveal a topological phase transition between a fractional Chern insulator (FCI) and a generalized Wigner crystal, distinguished by their structure factor signatures. We further calculate the quantum weight of various FCI states, verifying the universal topological bound derived by Onishi and Fu. Our findings provide new insights into the nature of phase transitions in strongly-correlated systems and establish a general framework for characterizing topological phases through structure factor analysis.