A study of the fractional quantum Hall energy gap at half filling.

摘要

A complete understanding of the nu = 52 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.;A crucial step towards verifying the Moore-Read description of the nu = 52 FQHE will be an unambiguous measurement of its spin state. In an effort to measure the 52 spin directly, we implemented a resistively detected nuclear magnetic resonance (RDNMR) technique. I report on our detailed study of the anomalous RDNMR lineshape around nu = 1, and discuss progress made towards measuring the 52 spin with this technique.;We studied the 52 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 52 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 52 state. We observe the 52 energy gap to collapse linearly with the in-plane field, whereas the neighbouring 73 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 52 FQHE.