Direct visualization and spectroscopic characterization of electrons’ wavefunctions have been the central interest of understanding the many-body states when electrons are strongly interacting with each other. By using the scanning tunneling microscopy/spectroscopy (STM/STS), one can achieve such tasks and study quantum materials with high spatial and energy resolution. Two-dimensional van der Waals heterostructure provides a great platform to explore exotic many-body states and study emergent phenomena. In this presentation, I will first show local spectroscopic studies on fractional quantum Hall states (FQHs) [1] and discuss the implications of fractionalization of electrons. In the second part, we demonstrate directly imaging the field-induced Wigner crystal [2] and the melting transition of these electron crystals as a function of electron densities. Interestingly, the crystal can melt into a FQH liquid and re-enter the crystalline phase. We will also discuss various types of Wigner crystals that emerge in the zeroth Landau level. In the last part of the presentation, I will present spectroscopic and imaging studies of strongly interacting Hofstadter’s states when subjected to a moiré potential by hBN alignment. We will analyze the symmetry breaking patterns of these topological states and visualize their melting transitions. Our work opens the door to examine a wide range of spatially modulated electronic phases with strong electron-electron interaction, as well as the visualization of fractionalized quasi-particles.
[1] Hu, Yuwen, et al. "High-resolution tunneling spectroscopy of fractional quantum Hall states." Nature Physics 21, 716–723 (2025)
[2] Tsui, Yen-Chen, et al. "Direct observation of a magnetic-field-induced Wigner crystal." Nature 628.8007 (2024): 287-292.