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

Abstract

The fractional quantum Hall (FQH) effect at filling factor ν = 5/2 has recently come under close scrutiny, as its ground state may possess quasi-particle excitations obeying nonabelian statistics, a property sought for topologically protected quantum operations. However, its microscopic origin remains unknown, and candidate model wave functions include those with undesirable abelian statistics. We report direct measurements of the electron spin polarization of the ν = 5/2 FQH state using resistively detected nuclear magnetic resonance. We find the system to be fully polarized, which unambiguously rules out the most likely abelian contender and lends strong support for the ν = 5/2 state being nonabelian. Our measurements reveal an intrinsically different nature of interaction in the first excited Landau level underlying the physics at ν = 5/2.

Localized NMR Mediated by Electrical-Field-Induced Domain Wall Oscillation in Quantum-Hall-Ferromagnet Nanowire

“…Although the experimental error depends on an uncertainty of ±5% in w, it is estimated to be about 0.32 MHz·nm for the ν = 2/3 state at 6.4 T, 6 which is translated into α full ∼ 0.38 MHz·nm at B = 7.65 T used in the present work. Meanwhile, it is shown that a tiny change of 0.3% in the in-plane electron density triggers the spin phase transition.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…The resonance at = 1, for instance, exhibits a strong asymmetry, whereas at = 2 the resonance is rather symmetric. This behavior can be understood as a consequence of the finite width of the electron wavefunction in the direction perpendicular to the quantum well as described below [159,184]. …”

“…Nevertheless, we deem the calibration at = 5 ⁄3 reliable. A spin polarization * ( = 1) < 1 is not surprising in view of the skyrmions present in this region (see section 3.2.2) and has been observed before [159,193]. In turn, using * ( = 1) = 1 as a calibration would imply * ( = 5 ⁄3) > 1/3, i.e.…”

“…It detects a characteristic shift of the nuclear resonance frequency in the presence of a spin polarized electron system. This technique has been employed in two similar studies, both of which found a fully spin polarized state [158,159].…”

“…The Knight shift depends on both the spin polarization and the electron densityin general the electron spin density. Over the last years, this technique has been established as a reliable method to probe the electron spin polarization [9,158,159,200]. The downside of this method in its current form is that it is only applicable at filling factors where depends on the Zeeman energy.…”