A thesis submitted to the Faculty of Science, University of the
Witwatersrand, Johannesburg, in fulfilment of the requirements for the
degree of PhD. August 9, 2017 / Nano-structured carbon lms, long studied due to the promise of exceptional quantum
transport properties, present a signi cant problem in condensed matter due to the disorder
which inherently forms in these materials. This work addresses the role of structural
disorder in low dimensional carbon systems. The in
uence of structural disorder on resonant
transmission is studied in diamond-like carbon superlattices. Having established a
model for disorder, this model for the structural changes is then applied to interpret experimental
measurements of diamond-like carbon superlattices. The role of phonons on
resonant transmission under a high frequency gate potential was also studied. This model
for structural disorder in heterogeneous carbon lms was then applied to disordered superconductors
close to the Anderson-Mott transition using the inhomogeneous Bogoliubov-de
Gennes theory. This analysis is then used in support of experimental work to understand
the superconductor-insulator transition in boron doped nano-crystalline diamond lms.
Coherent quantum transport e ects were demonstrated in structurally-disordered diamondlike
carbon (DLC) superlattices through distinct current modulation (step-like features) with
negative differential resistance in the current-voltage (I-V) measurements. A model for these
structurally disordered superlattices was developed using tight-binding calculations within
the Landauer-B uttiker formalism assuming a random variation of the hopping integral following
a Gaussian distribution. Calculations of the I-V characteristics for different con gurations
of superlattices compliment the interpretation of the measured I-V characteristics
and illustrate that while these DLC superlattice structures do not behave like conventional
superlattices, the present model can be used to tailor the properties of future devices. Furthermore
this tandem theoretical and experimental analysis establishes the validity of the
model for structural disorder.
The same model for the variation of disorder was then applied to interpret the electronic
transport properties of disordered graphene-like carbon thin films. The influence of disorder
on the activation energy in few layer graphitic lms was modelled and compared with experimental
observations through collaboration. The lms, grown by laser ablation, allowed
the speci c e ects of structural disorder in the sp2 - C phase to be probed. Defects acted as
effective barriers resulting in localization of charge carriers. Electron transmission spectra,
calculated with a tight-binding model, accounted for the change of localization length as a
result of disorder in the sp2 - C phase. This theoretical study showed that the localization
length of the thin graphitic lms can be tuned with the level of disorder and was shown to
be consistent with experimental studies.
The in
uence of nitrogen incorporation on resonant transmission in DLC superlattices
was then studied theoretically. This study illuminated the speci c role of the nitrogen
potential in relation to the Fermi level (EF ) in nitrogen incorporated amorphous carbon (a-
CN) superlattice structures. In a-CN systems, the variation of conductivity with nitrogen
percentage has been found to be strongly non-linear due to the change of disorder level.
The e ect of correlated carbon and nitrogen disorder was investigated in conjunction with
the nitrogen potential through analysis of transmission spectra, calculated using a tight
binding model, which showed two broad peaks related to these species. It was shown that
the characteristic transmission time through nitrogen centres can be controlled through a
combination of the nitrogen potential and correlated disorder. In particular, by controlling
the arrangement of the nitrogen sites within the sp2 - C clusters as well as their energetic
position relative to EF , a crossover of the pronounced transmission peaks of nitrogen and
carbon sites can be achieved. Furthermore, it was shown that nitrogen incorporated as a
potential barrier can also enhance the transmission in the a-CN superlattice structures. The
strong non-linear variation of resistance and the characteristic time of the structures can
explain the transport features observed experimentally in a-CN fi lms.
This analysis was then partnered with measurements performed on nitrogen-incorporated
carbon superlattices (N-DLC QSL) by Neeraj Dwivedi (National University of Singapore).
The electrical characteristics of these nitrogen incorporated superlattice devices revealed
prominent negative di erential resistance (NDR) behavior. The interpretation of these
measurements was supported by 1D tight binding calculations of disordered superlattice
structures (chains), which included signi cant bond alternation in sp3-hybridized regions.
This analysis showed improved resonant transmission, which can be ascribed to nitrogendriven
structural modi cation of the N-DLC QSL structures, especially the increased sp2-C
clustering that provides additional conduction paths throughout the network.
In order to determine the in
uence of additional factors on coherent quantum states in
molecular systems as an extension to the analysis on superlattices, a theoretical study of
the electron-phonon interaction in double barrier structures under the in
uence of a timedependent
gate potential was undertaken. The Floquet theory was employed along with
expansion in a polaron eigenbasis to render a multi-dimensional single body problem. An
essentially exact solution was found using the Riccati matrix technique. It was demonstrated
that optimal transmission can be achieved by varying the frequency of the gate potential.
In addition, it was shown that the gate potential can be used to control the energy of the
resonant states very precisely while maintaining optimal transmission.
Having gained a deep understanding of the structural changes induced in carbon systems
through the incorporation of nitrogen, a similar structural model was then applied
to study the changes induced in diamond and nanocrystalline fi lms by boron incorpora-
tion. Boron doped diamond provides an interesting superconductor with ongoing debate
surrounding the nature of the impurity band and the effect on the superconducting phase
transition of structural changes induced by boron incorporation. The in
uence of disorder,
both structural (non-diagonal) and on-site (diagonal), was studied through the inhomogeneous
Bogoliubov-de Gennes (BdG) theory in narrow-band disordered superconductors
with a view towards understanding superconductivity in boron doped diamond (BDD) and
boron-doped nanocrystalline diamond (B-NCD) lms. We employed the attractive Hubbard
model within the mean eld approximation, including a short range Coulomb interaction
between holes in the narrow acceptor band. We studied substitutional boron incorporation
in a triangular lattice, with disorder in the form of random potential
uctuations at the
boron sites. The role of structural disorder was investigated through non-uniform variation
of the tight-binding coupling parameter where, following experimental ndings in BDD and
B-NCD lms, we incorporated the concurrent increase in structural disorder with increasing
boron concentration.
Stark differences between the ffects of structural and on-site disorder were demonstrated
and showed that structural disorder has a much greater e ect on the density of states, mean
pairing amplitude and super
uid density than on-site potential disorder. We showed that
structural disorder can increase the mean pairing amplitude while the spectral gap in the
density of states decreases, with states eventually appearing within the spectral gap for high
levels of disorder. This study illustrated how the effects of structural disorder can explain
some of the features found in superconducting BDD and B-NCD lms, such as a tendency
towards saturation of the critical temperature (Tc) with boron doping and deviations from
the expected Bardeen-Cooper-Shrie er (BCS) theory in the temperature dependence of the
pairing amplitude and spectral gap. The variation of the super
uid density considering only
structural disorder was markedly different from the variation with on-site disorder only and
revealed that structural disorder is far more detrimental to superconductivity and accounts
for the relatively low Tc of BDD and B-NCD in comparison to the Tc predicted using the
conventional BCS theory.
This theoretical work was then used to interpret features in the measured transport
properties of B-NCD lms with di erent doping concentrations and microstructures. The
temperature dependence of a distinct local maximum in eld dependent magnetoresistance
measurements showed suppression of the density of states as the system breaks up into superconducting
regions separated by grain boundaries. Differential resistance measurements
at different temperatures and magnetic fi elds showed a transition from a local minimum at
zero applied current, indicative of persisting superconducting regions, to a local maximum.
A power law dependence over a certain current range in the measured I-V characteristics
at di erent magnetic elds suggests a Berezinski-Kosterlitz-Thouless (BKT) transition. In
addition, features in the magnetoresistance clearly indicate additional phases. Together
with features in current-voltage measurements, these signatures show the coexistence of
superconductivity and additional competing phases close to the Anderson-Mott transition. / LG2018
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/25118 |
| Date | January 2017 |
| Creators | McIntosh, Ross William |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (178 pages), application/pdf |
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