Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

Numerical algorithms for computing the electronic structure of incommensurate 2D-materials using ab initio models are critical for predicting material properties and guiding experiments. For bilayers, momentum space and continuum models have been introduced to approximate observables of ab initio tight-binding models using a momentum description, despite the lack of periodicity in the tight-binding model required for Bloch theory. A similar structure has been introduced for double-incommensurate trilayers using a continuum model, where the three lattices are mutually incommensurate. However, this description leads to a four-dimensional lattice space, and numerical convergence of the density of states has been observed to be very slow. In this work, we introduce a momentum space framework for double-incommensurate trilayer graphene, and we introduce an efficient truncation scheme for the four-dimensional lattice to drastically improve the convergence of the regularized density of states and the regularized local density of states (a parallel object to classical band structure). We implemented this algorithm on an ab initio model of twisted trilayer graphene and validated the convergence estimates. ix

Date

5-11-2026

Committee Chair

Shipman, Stephen

LSU Acknowledgement

1

LSU Accessibility Acknowledgment

1

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