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Spin polarization of the 5/2 fractional quantum Hall state

The fractional quantum Hall (FQH) effect observed in a high quality 2 dimensional electron gas (2DEG) at low temperatures and high magnetic fields is a direct manifestation of electron-electron interactions, which open energy gaps in the density of states for certain fractional occupation of the Landau levels. Fractional quantum Hall states observed for odd denominator fractions are now well understood within the framework of the Laughlin wavefunction, whose quasiparticles carry fractional charges and exhibit quantum statistics which are neither Fermionic nor Bosonic, but the so-called “anyonic” statistics.

Even more exotic is the Moore-Read “Pfaffian state” proposed to account for the only even denominator FQH state observed when the filling factor of the Landau levels is equal to 5/2. The Moore-Read state indeed gives rise to excitations whose statistics are not described by a simple phase factor under adiabatic exchange, but rather by a matrix operator, which is not commutable. These statistics are termed non-abelian anyonic statistics. On its own, the observation of these new kind of quantum statistics would represent a milestone in physics. In recent years, the Moore-Read wavefunction has received further major interest owing to the fact that non-abelian quantum statistics would underly a new paradigm for topological (fault tolerant) quantum computation. In spite of several important theoretical advancements however, an unequivocal experimental verification of the Moore-Read description is still missing. In particular, the p-wave symmetry of this wave function, imposing the full spin polarization of electron in this state, has been the subject of intense debates and experimental efforts over the last 20 years.

Using Resistively Detected Nuclear Magnetic Resonance (RDNMR) at very low temperature, we have measured the sought-after spin polarization of this state. In agreement with the Moore-Read theory, electron are fully spin polarized in the 5/2 fractional quantum Hall state, which is also in-line with recent experiments performed on a different sample [L.Tiemann et al, Science. 335, 828 (2012)]. The full spin polarisation is a necessary condition for the validity of the Moore-Read theory, and electronic interferometric experiments will now have to determine the nature of quantum statistics in this state.

For more details on our experiment, please take a look at the related PRL article.