Visualizing structure of correlated ground states using collective charge modes

The variety of correlated phenomena in moir\'e systems is incredibly rich, spanning effects such as superconductivity, a generalized form of ferromagnetism, or even charge fractionalization. This wide range of quantum phenomena is partly enabled by the large number of internal degrees of freedom in these systems, such as the valley and spin degrees of freedom, which interplay decides the precise nature of the ground state. Identifying the microscopic nature of the correlated states in the moir\'e systems is, however, challenging, as it relies on interpreting transport behavior or scanning-tunneling microscopy measurements. Here we show how the real-space structure of collective charge oscillations of the correlated orders can directly encode information about the structure of the correlated state, focusing in particular on the problem of generalized Wigner crystals in moir\'e transition metal dichalcogenides. Our analysis builds upon our earlier result [10.1126/sciadv.adg3262] that the presence of a generalized Wigner crystal modifies the plasmon spectrum of the system, giving rise to new collective modes. We focus on scanning near-field optical microscopy technique (SNOM), fundamentally a charge-sensing-based method, and introduce a regime under which SNOM can operate as a probe of the spin degree of freedom.