Abstract

Moiré quantum materials have emerged as a highly tunable platform for studying strongly interacting electrons in low dimensions. By twisting or lattice-mismatching atomically thin crystals, one can generate long-wavelength moiré superlattices that reconstruct the electronic bands, produce narrow bandwidths, and greatly enhance the importance of Coulomb interactions. As a result, these systems host a wide range of correlated phenomena, including symmetry breaking, magnetism, and superconductivity. This dissertation develops and applies Green's-function-based many-body methods to understand the role of interactions in moiré quantum materials. This dissertation consists of four chapters. The first chapter introduces moiré quantum materials and reviews the basic theoretical framework used throughout the thesis, including continuum models, many-body perturbation theory, and Migdal-Eliashberg theory. The second chapter develops a many-body perturbation theory framework for moiré systems in the Bloch basis, allowing a systematic treatment of interaction effects beyond static Hartree-Fock theory. Using twisted bilayer graphene as a case study, I derive analytical results for symmetry-breaking states in the chiral-flat limit, study finite-temperature gap closing, and incorporate self-consistent GW corrections to examine the role of dynamical screening and correlation effects. The third chapter applies Hartree-Fock theory to twisted bilayer WSe2 and MoTe2, with emphasis on the role of lattice relaxation and interaction-driven magnetism. I construct realistic continuum models from ab initio-motivated parameters and determine the emergence of ferromagnetic and antiferromagnetic phases as functions of filling, displacement field, interaction strength, and twist angle. The results clarify how the interplay between moiré band structure, layer polarization, and Coulomb interactions controls magnetic order in twisted transition metal dichalcogenides. The fourth chapter studies plasmon-mediated superconductivity in twisted bilayer graphene and the effect of external screening gates. By solving the full frequency-dependent Eliashberg equations, I analyze how dynamical screening and plasmon energy scales determine the superconducting critical temperature. I show that nearby screening gates can strongly modify the effective interaction while leaving the critical temperature comparatively robust over experimentally relevant regimes, providing a theoretical explanation for this stability. Together, these studies provide a unified microscopic description of how interactions reshape band structure and generate collective electronic phases in moiré quantum materials.

Committee Chair

Shaffique Adam

Committee Members

Alexander Seidel; Erik Henriksen; Li Yang; Rohan Mishra

Degree

Doctor of Philosophy (PhD)

Author's Department

Physics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

4-27-2026

Language

English (en)

Author's ORCID

https://orcid.org/0000-0002-2102-674X

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