Quantum Two Dimensional Materials Explored via Advanced Electron Microscopy

Two dimensional (2D) materials often exhibit unexpected, emergent physical properties—often due to their confined dimensionalities and unique symmetry breaking. However, 2D materials still exist in the 3D world. They often consist of multiple atomic layers, not perfectly flat, and interact with environment above and below. Therefore, understanding of full 3D structure of 2D materials is paramount to harnessing the true potential of 2D materials. In this dissertation, we will discuss advanced electron microscopy techniques to probe various 2D materials and heterostructures thereof. We engineer periodically modulated out-of-plane interaction by forming moiré patterns of 2D materials. Furthermore, this work demonstrates 2D endotaxy of tantalum disulfides (TaS₂) and endotaxial polytype heterostructure as a new platform to stabilize latent CDW states. Chapter I and II motivates electron microscopy and electron diffraction for probing atomic structure of 2D materials in real spaces. It also discusses rich information hidden in 3D reciprocal structures of 2D materials and introduces 3D electron diffraction as a platform for probing 3D reciprocal structures. We use 3D electron diffraction to measure and identify various out-of-plane information of multiple 2D materials. We measure inter- and intra-layer spacings in 2-layer graphene, 1-layer molybdenum disulfide (MoS₂), identify exact stacking sequence of 6 and 12-layer graphenes and measure small lattice distortions. In Chapter III, periodic lattice distortions (PLDs) in twisted 2D materials are discussed. Moiré pattern emerges when two layers of 2D materials are stacked with a mismatch in crystal orientation. This results in periodically modulated out-of-plane interactions which periodically distorts constituent 2D crystals. Here, we introduce torsional PLD to describe the periodic restructuring in twisted 2D materials and extract a single coefficient that describes the full restructuring scheme by matching experimental data to computationally simulated data. With torsional PLD, we describe positions of >10,000 atoms in 1.1° twisted bilayer graphene using a single order parameter. Lastly, we showcase various twisted 2D materials that exhibits torsional PLD. In Chapter IV and V, we discuss charge density waves (CDWs) in 2D materials. We introduce the novel method of endotaxial engineering that manipulates CDW phases. Specifically, in Chapter IV, we show endotaxial polytype engineering stabilizes low temperature long-range ordered CDW phase at room temperatures and enables out-of-plane twinning in octahedrally coordinated TaS₂. We provide a theoretical model explaining twinning of CDWs as well as a computational validation. In Chapter V, we investigate the nature of incommensurate CDWs in TaS₂. We show endotaxial polytype engineering crystallizes IC-CDWs into more long-range ordered and amplitude enhanced version. We also reveal the hexatic nature of the IC-CDWs in TaS₂ by doing controlled heating experiments. Lastly, Chapter VI summarizes result and concludes this thesis.PhDMaterials Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/177918/1/sukhsung_1.pd