Dissertation/Thesis Abstract

Landau Level Mixing Effects on Fractional Quantum Hall Energies in Graphene via Monte Carlo
by Hernandez, Uriel Fernando, M.S., California State University, Long Beach, 2019, 100; 22587621
Abstract (Summary)

The effect of Landau level mixing of graphene under fractional quantum Hall effect conditions is examined theoretically. A parallelized Monte Carlo program is developed to obtain estimates for the expectation values of the ground state energy eigenstates of composite fermion wavefunctions in the lowest Landau level where the emergent three-body terms due to Landau level mixing vanish exactly. To incorporate the effects of Landau level mixing on the remaining two-body terms of the Hamiltonian, an effective potential V_{eff}=1/r+\sum_{i=0}^{M}C_{i}r^{i}e^{-r} is used to model the interaction. The Monte Carlo program is benchmarked by comparing its results to those obtained via exact diagonalization using effective Haldane pseudopotentials. Energy estimates for filling factors ν = 1/3, 2/5, and 3/7 are obtained and analyzed for various system sizes and strength of Landau level mixing. Estimates for the energies in the thermodynamic limit are obtained using two different methods.

Indexing (document details)
Advisor: Peterson, Michael R
Commitee: Ojeda-Aristizabal, Claudia, Pickett, Galen
School: California State University, Long Beach
Department: Physics and Astronomy
School Location: United States -- California
Source: MAI 81/4(E), Masters Abstracts International
Subjects: Physics, Computational physics, Condensed matter physics
Keywords: FQHE, Graphene, Landau level mixing, Monte Carlo, Physics
Publication Number: 22587621
ISBN: 9781687913579
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