Physics
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Item Computational and Analytical Investigations of Disordered and Interacting Systems(2013) Biddle, John Charles; Das Sarma, Sankar; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Localization of particle wavefunctions in quasi-disordered one dimensional incommensurate lattices is studied both numerically and analytically. Through exact diagonalization, we show that energy dependent mobility edges can appear in the case of shallow lattices. We also show that these mobility edges can be studied with a tight-binding model (an extension of the Aubry-Andre model) that has energy dependent mobility edges that can be determined analytically. Topological aspects of the Aubry-Andre/Harper model are also studied by numerically calculating the Chern number. We first verify arguments by numerical calculations that variations in the Chern density decrease with increasing system size when the potential is incommensurate with the lattice. Next we introduce random disorder into the model and study the Chern number and the Chern density as a function of disorder strength by using the non-commutative Brillouin zone. We show that variations of the Chern density take on the same trends for both commensurate and incommensurate potentials after some critical disorder strength is reached. Strongly correlated quantum Hall states are also examined. We numerically examine the entanglement entropy and the entanglement spectrum of fractional quantum hall states as a function of the finite layer thickness $d$ of the quasi-two-dimensional system for a number of filling fractions $\nu$ in the lowest and the second Landau levels: $\nu$ = 1/3, 7/3, 1/2, and 5/2. We observe that the entanglement measures are dependent on which Landau level the electrons fractionally occupy and are completely consistent with the results based on wavefunction overlap calculations. We also compare the ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point. Our results suggest that even under moderate deviations in the interaction potential the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half filled SLL, consistent with recent experimental investigations.Item CHARGE TRANSPORT IN GRAPHENE WITH ADATOM OVER-LAYERS ; CHARGED IMPURITY SCATTERING, DIELECTRIC SCREENING, AND LOCALIZATION.(2011) Jang, Chaun; Fuhrer, Michael S; Physics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Graphene, a single atom thick plane of graphite, is a novel two-dimensional electron system in which the low-energy electrons behave as massless chiral Dirac fermions. This thesis explores the effects of disorder in graphene through controlled surface modification in ultra-high vacuum (UHV), coupled with in situ electronic transport experiments. Three different roles of adatom overlayers on graphene are investigated. First, the effects of charged impurity scattering are studied by introducing potassium ions on the graphene at low temperature in UHV. The theoretically expected magnitude and linear density-dependence of the conductivity due to long range Coulomb scattering is verified. Second, the effective dielectric constant of graphene is modified by adding ice overlayers at low temperature in UHV. The opposing effects of screening on scattering by long range (charged impurity) and short range impurities are observed as variations in conductivity, and the changes are in agreement with Boltzmann theory for graphene transport within the random phase approximation. The minimum conductivity of graphene is roughly independent of charged impurity density and dielectric constant, in agreement with the self-consistent theory of screened carrier density inhomogeneity (electron and hole puddles). Taken together, the experimental results on charged impurity scattering and dielectric screening strongly support that long range Coulomb scattering is the dominant scattering mechanism in as-fabricated graphene on SiO2. In addition to the semi-classical transport properties, quantum transport is also studied with cobalt decorated graphene. Strong localization is achieved in the disordered graphene through deposition of cobalt nanoclusters. In finite magnetic field a phase transition occurs from the localized state to the quantum Hall state. Scaling analysis confirms that the transition is a quantum phase transition which is similar to the localization - delocalization transitions in other two dimensional electron systems.