A complete understanding of the the ν = 5/2 fractional quantum hall effect (FQHE) continues to be among the most exciting problems in semiconductor physics. It is widely believed that this unique electron state is described by the Moore-Read Pfaffian wavefunction, resulting from a BCS-like pairing of composite fermions. In recent years this wavefunction has received special interest owing to its non-abelian quantum statistics which underlies a new paradigm for fault tolerant quantum computation. However, in spite of several theoretical advancements, an unequivocal experimental verification of the Moore-Read description is still missing. We studied the 5/2 state in a very high quality 2DEG sample with the lowest electron density reported to date, by nearly a factor of two. We demonstrate that large discrepancies between experimentally measured values of the 5/2 energy gap, and theoretical calculations based on the Moore-Read theory, can not be trivially attributed to disorder as has conventionally been assumed. Using a tilted field geometry, we investigated the effect of applying an in-plane magnetic field on the 5/2 state. We observe the 5/2 energy gap to collapse linearly with the in-plane field, whereas the neighbouring 7/3 shows a strong enhancement. The opposite behaviour between the two states is in startling contrast to theory which predicts both gaps should be similarly suppressed. Since the early theoretical foundation in support of the Moore-Read interpretation presumed the two states should behave the same, our experimental finding of opposite behaviour may necessitate a fundamental rethinking of the nature of the 5/2 FQHE. A crucial step towards verifying the Moore-Read description of the ν = 5/2 FQHE will be an unambiguous measurement of its spin state. In an effort to measure the 5/2 spin directly, we implemented a resistively detected nuclear magnetic resonance (RDNMR) technique. I report on our detailed study of the anomalous RDNMR lineshape ar / Une compr\'ehension compl\`ete de l'effet Hallquantique fractionnaire (EHQF) \`a $\nu = \frac$ continue \`afaire partie des probl\`emes les plus passionnants de la physiquedes semi-conducteurs. On estime g\'en\'eralement que cet \'etat\'electronique unique est d\'ecrit par la fonction d'onde deMoore-Read connue sous le nom de ``Pfaffien'', r\'esultant d'unappariement de type BCS de fermions composites. Cette fonctiond'onde a r\'ecemment suscit\'e un int\'er\^et tout particulier enraison de ses statistiques quantiques non-ab\'eliennes quisous tendent un nouveau paradigme pour le calcul quantique insensibleaux d\'efaillances. En d\'epit de plusieurs avanc\'ees th\'eoriques,il manque toutefois une v\'erification exp\'erimentaled\'efinitive de la description Moore-Read.Nous avons \'etudi\'e l'\'etat $\frac$ dans un gaz\'electronique bidimensionnel de tr\`es haute mobilit\'e ayant laplus faible densit\'e d'\'electrons report\'ee \`a ce jour, cecide par un facteur proche de deux. Nous d\'emontrons que lesimportants \'ecarts entre les valeurs du gap d'\'energie \`a$\frac$ mesur\'ees exp\'erimentalement et les calculsth\'eoriques bas\'es sur la th\'eorie Moore-Read ne peuvent pas\^etre uniquement attribu\'es au d\'esordre, comme cela atraditionnellement \'et\'e propos\'e. En utilisant un champ \`ag\'eom\'etrie inclin\'ee, nous avons \'etudi\'e l'effet del'application d'un champ magn\'etique dans le plan sur l'\'etat$\frac{5}{2}$. Nous observons une d\'ecroissance lin\'eaire du gapd'\'energie \`a $\frac$ en fonction du champ magn\'etiquedans le plan, tandis que le gap d'\'energie d'\'etat fractionnairevoisin $\frac{7}{3}$ exhibe une forte augmentation. Lecomportement oppos\'e des deux \'etats est en contraste avec lath\'eorie qui pr\'evoit que les deux gaps doivent \^etresupprim\'es par l'application d'un champ magn\'etique dans le plan, ce quin\'ecessite un nouvel examen de la nature de l'EHQF$\frac$.Une \'etape cruciale vers la v\'erificati
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.40784 |
| Date | January 2009 |
| Creators | Dean, Cory |
| Contributors | Guillaume Gervais (Internal/Supervisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | Electronically-submitted theses. |
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