Yanxing Li Final Defense

Abstract: Electron correlation and topology are two fundamental pillars of quantum materials. The advent of low-dimensional materials has provided a transformative platform for their confluence, enabling the tuning of rich parameters to engineer band flatness, quantum geometry, and emergent correlated states. A two-dimensional (2D) example is moiré materials, formed by stacking two and more van der Waals layers with a relative rotation or lattice misalignment, resulting in a moiré superlattice (MSL) leading to strong Coulomb interactions and exotic quantum phases. These correlated phases manifest as incompressible quantum Hall liquids, generalized Wigner crystal solids, and (fractional) Chern insulator states, depending on the tunable parameters, in systems such as twisted bilayer graphene and transition metal dichalcogenides. The one-dimensional (1D) example is Tomonaga-Luttinger liquids (TLL), which emerge in 2D boundaries, edge states of quantum Hall systems, and moiré 1D channels. In this gapless quantum liquid, the strong electron correlations break down Fermi liquid theory, leading to spin-charge separation. Identifying and understanding these phases is pivotal for advancing our knowledge of exotic quantum phenomena and their potential applications.

In this defense, we explore the interplay between electron correlations and flat-band formation in twisted WSe₂ bilayers and WSe₂ monolayer antiphase boundaries. For the 2D MSL system, we investigate the twist-angle-dependent properties. In small-angle MSLs, our focus is on systems where layer pseudospin textures dominate moiré band topology. In large-angle moiré platforms, we examine two distinct regimes: (1) the transition from short-period moiré crystals to long-wavelength super-moiré structures near commensurate angles, and (2) the formation of moiré quasicrystals, where broken translational symmetry invalidates the Bloch theorem. For the 1D system, represented by TLL quantum dot chains, we report intra-TLL Coulomb interactions and inter-TLL coupling effects.