UC Berkeley

Strongly correlated electrons in two dimensions can crystallize into a Wigner solid, and the melting of this electron crystal as carrier density is tuned offers a direct window into the interplay of correlations, disorder, and quantum fluctuations. Two-dimensional moiré heterostructures have emerged as a uniquely flexible platform for stabilizing and probing such crystals, but most prior studies have accessed them only through bulk transport or optical measurements that average over the spatial inhomogeneity. In this dissertation, scanning tunneling microscopy (STM) is used to image Wigner crystals and their quantum melting in engineered moiré potentials. An introduction to the field, device fabrication procedures, and scanning tunneling microscopy are described in the initial chapters. Experimental measurements are discussed in the subsequent chapters that cover different regimes: the quantum melting of generalized Wigner crystals in a strong periodic potential, the quantum melting of bare Wigner crystals into correlated liquid-like phases, and quantum melting of a Wigner crystal in a weak periodic potential, which realizes a two-dimensional Frenkel-Kontorova model. An outlook towards STM-coupled high-frequency measurements of gate-tunable 2D heterostructures is provided in the end. Together these results establish local imaging as a powerful probe for understanding the quantum melting of correlated electron phases in two dimensions.