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Disorder and interactions in graphene and other quantum systems
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Fischer, Andrea M. (2011) Disorder and interactions in graphene and other quantum systems. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2491316~S15
Abstract
This thesis examines the topics of disorder and electron-electron interactions
in three distinct quantum systems. Firstly, the Anderson transition is studied for
the body centred cubic and face centred cubic lattices. We obtain high precision
results for the critical disorder at the band centre and the critical exponent using
the transfer-matrix method and finite size scaling. Comparing the critical disorder
between the simple cubic, body centred cubic and face centred cubic lattices, an
increase in the critical disorder is observed as a function of the coordination number
of the lattice. The critical exponent is found to be v ≃ 1:5 in agreement with the
value for the simple cubic lattice. Energy-disorder phase diagrams are plotted for
both lattice types.
Next, we consider the Aharonov-Bohm effect for an exciton in a 1D ring
geometry. The aim is to determine how the addition of a constant electric field
in the plane of the ring effects the Aharonov-Bohm oscillations, which occur as
a function of the magnetic
ux threading the ring. We develop a self consistent
equation for the ground state energy, which is then solved numerically. Oscillations
in the ground state energy have an increasing amplitude as a function of electric
field strength until a critical electric field value. At this point, oscillations in the
oscillator strength become inverted, with the oscillation minimum reaching zero at
half a magnetic
ux quantum. This suggests a possible process for controlling the
formation and recombination of excitons through tuning the applied fields.
The final and largest section of the thesis is concerned with collective excitations
of graphene in a strong perpendicular magnetic field. The excitations, which
are most strongly mixed are identified and used as a basis to diagonalise the Hamiltonian,
which includes the Coulomb interaction between electrons and holes. In this
way the oscillator strengths and energies of collective excitations are obtained. The
good quantum numbers for collective excitations are identified. In particular, we
study those arising from the SU(4) symmetry, which is due to two spin and two
valley pseudospin projections. This enables us to determine the multiplet structure
of the states. In addition to neutral collective excitations or excitons, we investigate
the possible formation of charged collective excitations or trions from nearly full or
nearly empty Landau levels. The localisation of neutral collective excitations upon
a single Coulomb or δ-function impurity is also examined.
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QC Physics | ||||
Library of Congress Subject Headings (LCSH): | Quantum theory, Electron-electron interactions, Order-disorder models, Graphene | ||||
Official Date: | January 2011 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Department of Physics | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Römer, Rudolf | ||||
Sponsors: | Engineering and Physical Sciences Research Council (EPSRC) ; University of Warwick ; Institute of Physics (Great Britain) ; C. R. Barber Trust | ||||
Extent: | xv, 151 leaves : ill., charts | ||||
Language: | eng |
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