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Date Available

5-13-2025

Year of Publication

2025

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy (PhD)

College

Arts and Sciences

Department/School/Program

Physics and Astronomy

Faculty

Ganpathy Murthy

Faculty

Anatoly Dymarsky

Abstract

In the presence of a perpendicular magnetic field, monolayer graphene at and near charge neutrality forms a quantum Hall ferromagnet—a correlated electronic state where the interplay of interactions, spin, and valley degrees of freedom leads to spontaneous symmetry breaking. While the dominant Coulomb interaction has $SU(4)$ symmetry, the ground state is ultimately determined by subdominant terms: residual lattice-scale anisotropic interactions, Zeeman, and sublattice couplings. Relaxing the ultra-short-range limit of anisotropic interactions unveils diverse symmetry-breaking phases in both integer and fractional quantum Hall regimes. Haldane pseudopotentials, which quantify interactions between particle pairs with fixed relative angular momentum, provide a readily parameterizable framework for anisotropic interactions, enabling the construction of a variational energy functional via the combined use of exact diagonalization and Hartree-Fock approximation. In this thesis, we systematically explore emergent symmetry-breaking phases at both integer and fractional fillings in monolayer graphene Landau levels.

Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2025.202

Funding Information

This study was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC-0024346.

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