Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The experimental observation of the quantum Hall effect in a two-dimensional electron gas posed
an intriguing question to theorists: Why is the quantization of conductance so precise, given the
imperfections of the measured samples? The question was answered a few years later, when a
connection was uncovered between the quantum Hall effect and topological quantities associated
with the band structure of the material in which it is observed. The Hall conductance was revealed
to be an integer topological invariant, implying its robustness to certain perturbations.
The topological theory went further than explaining only the usual integer quantum Hall effect
in a perpendicular magnetic field. Soon it was realized that it also applies to certain systems in
which the total magnetic flux is zero. Thus it is possible to have a quantized Hall effect without
Landau levels.
We study a carbon nanotube in a magnetic field perpendicular to its axial direction. Recent
studies suggest that the application of an electric field parallel to the magnetic field would induce
a gap in the electronic spectrum of a previously metallic carbon nanotube. Despite the quasi onedimensional
nature of the carbon nanotube, the gapped state supports a quantum Hall effect and
is associated with a non zero topological invariant. This result is revealed when an additional
magnetic field is applied parallel to the axis of the carbon nanotube. If the flux due to this
magnetic field is varied by one flux quantum, exactly one electron is transported between the
ends of the carbon nanotube. / AFRIKAANSE OPSOMMING: Die eksperimentele waarneming van die kwantum Hall effek in ’n twee-dimensionele elektron gas
laat ’n interessante vraag aan teoretiese fisikuste: Waarom sou die kwantisasie van die geleiding
so presies wees al bevat die monsters, waarop die meetings gedoen word, onsuiwerhede? Hierdie
vraag word ’n paar jaar later geantwoord toe ’n konneksie tussen die kwantum Hall effek en
topologiese waardes, wat verband hou met die bandstruktuur van die monster, gemaak is. Dit
is aan die lig gebring dat die Hall geleiding ’n heeltallige topologiese invariante is wat die robuustheid
teen sekere steurings impliseer. Die topologiese teorie verduidelik nie net die gewone
kwantum Hall effek wat in ’n loodregte magneetveld waargeneem word nie. Dit is ook moontlik
om ’n kwantum Hall effek waar te neem in sekere sisteme waar die totale magneetvloed nul is.
Dit is dus moontlik om ’n gekwantiseerde Hall effek sonder Landau levels te hˆe.
Ons bestudeer ’n koolstofnanobuis in ’n magneetveld loodreg tot die aksiale rigting. Onlangse
studies dui daarop dat die toepassing van ’n elektriese veld parallel aan die magneetveld ’n
gaping in die elektroniese spektrum van ’n metaliese koolstofnanobuis induseer. Ten spyte van
die een-dimensionele aard van die koolstofnanobuis ondersteun die gapings-toestand steeds ’n
kwantum Hall effek en hou dit verband met ’n nie-nul topologiese invariante. Hierdie resultaat
word openbaar wanneer ’n bykomende magneetveld parallel tot die as van die koolstofnanobuis
toegedien word. Indien die vloed as gevolg van hierdie magneetveld met een vloedkwantum
verander word, word presies een elektron tussen die twee kante van die koolstofnanobuis vervoer.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71643 |
| Date | 12 1900 |
| Creators | Brand, Janetta Debora |
| Contributors | Snyman, Izak, Stellenbosch University. Faculty of Science. Dept. of Physics. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | vii, 79 p. : ill. |
| Rights | Stellenbosch University |
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