Unraveling the Spin Polarization of the = 5/2 Fractional Quantum Hall State

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Lars Tiemann1, 2, Gerardo Gamez1, Norio Kumada1, and Koji Muraki1, 2
1Physical Science Laboratory, 2Japan Science and Technology Agency

@Fundamental particles in nature are classified as either fermions or bosons according to how the wave function changes sign with interchange of two particles. Remarkably, behavior of particles in a correlated state is often described in terms of quasiparticles possessing properties different from those of the original particles. In two dimensions, a quasiparticle behaving differently from fermions or bosons is theoretically possible. In particular, theory predicts the existence of quasiparticles with exceedingly unusual properties. These quasiparticles, known as non-Abelian quasiparticles, whose interchange takes the system from one of its many ground states to another, have attracted strong interest from both theory and experiment as it would establish the foundation for topological quantum computing-an entirely novel architecture for error free quantum computation [1].
@Fractional quantum Hall states that emerge in a two-dimensional electron system confined to a heterointerface of pristine semiconductor crystals, such as GaAs/AlGaAs, are expected to host such exotic quasiparticles that are neither fermions or bosons. Of particular interest is the one at Landau level filling factor = 5/2 [2], which is predicted to support non-Abelian quasiparticles. However, unlike other states, the exact origin of the = 5/2 state remains unknown. The likely candidates for its wave function that emerged through experiment [3] include one that does not support non-Abelian quasiparticles. Exploiting the fact that these wave functions have different spin states, we have demonstrated for the first time that all the electrons in the = 5/2 state have their spins fully polarized along the applied field using resistively detected nuclear magnetic resonance (NMR) (Fig. 1) [4]. With our results, possible theoretical models are narrowed down to only those supporting non-Abelian quasiparticles.

[1] C. Nayak et al., Rev. Mod. Phys. 80 (2008) 1083.
[2] R. L. Willet et al., Phys. Rev. Lett. 59 (1987) 1779.
[3] I. P. Radu et al., Science 320 (2008) 899.
[4] L. Tiemann, G. Gamez, N. Kumada, and K. Muraki, Science 335 (2012) 828.
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Fig. 1. (a) Longitudinal resistance (Rxx) versus gate voltage.
(b) Resistively detected NMR spectra of 75As measured at 6.4 T at = 2, 5/2 and 5/3.
Insets show the measurement set up (left) and the spin configuration at each (right).

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