Kaxiras, EfthimiosFang, Shiang2019-12-122019-052019-04-242019Fang, Shiang. 2019. Multi-scale Theoretical Modeling of Twisted van der Waals Bilayers. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029747Two-dimensional layered materials are an interesting class of quantum materials. Since the discovery of exfoliated single-layer graphene, more types of two-dimensional layered materials have been investigated. In contrast to conventional crystalline materials, these layered materials can be stacked together to form new heterostructures with new properties. In recent experiments, the twisted bilayer graphene is shown to display unconventional insulating and superconducting phases when rotated at the magic twist angle. One advantage of these layered heterostructures as a new pathway to interacting electrons is the various control knobs available in experiments such as the pressure and external fields. To overcome the challenges in the theoretical descriptions of these complicated heterostructure systems, we develop an ab initio multi-scale numerical method that combines the density functional theory calculations and Wannier functions. With these accurate ab initio models, the effective Hamiltonians can be derived for efficient calculations. This framework allows us to simulate various control knobs in the experiments and generalize to other layer types.application/pdfenTwo-dimensional layered materialsgraphenetwisted bilayermulti-scale simulationvan der Waals heterostructureThesis or Dissertation2019-12-120000-0002-9412-6426