Ab initio methods for non-periodic 2D layered materials: from misfits, through intercalation, to quasicrystals
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The theoretical description of materials has traditionally relied on discrete translational symmetry, enabling crystalline solids to be represented by periodic unit cells and treated using Bloch’s theorem within conventional band theory. However, many systems of interest, such as lattice mismatched heterostructures, intercalated materials, and twisted 2D quasicrystals, lack such symmetry and admit no finite periodic representation, frustrating the application of standard first-principles methods like density functional theory (DFT). In this thesis, I develop and apply a class of ab initio methods for accurately treating non-periodic layered materials, considering both in-plane and out-of-plane disorder. First, I introduce a framework based on the principle of nearsightedness to compute observable properties of layered heterostructures expressible as integrals of spectral functions, avoiding the artificial strain inherent to conventional DFT. Applying this method to (LaSe)1.14(NbSe2)2, I identify an unexpected mechanism responsible for its large observed doping. I then investigate the role of intercalation in modifying the material stacking, uncovering multiple intercalant induced stacking transitions, and study their impact on thermoelectric transport in Bi2Se3 through enhanced anharmonicity and stacking fault scattering. Finally, I extend the framework to construct locally ab initio Wannier Hamiltonians for arbitrary incommensurate materials, demonstrating this extension by reproducing the subtle electronic features of quasicrystalline 30° twisted bilayer graphene arising from interlayer hybridization.