NMR Probing of the Spin Polarization of theν=5/2Quantum Hall State

Abstract

Resistively detected nuclear magnetic resonance is used to measure the Knight shift of the 75 As nuclei and determine the electron spin polarization of the fractional quantum Hall states of the second Landau level. We show that the 5/2 state is fully polarized within experimental error, thus confirming a fundamental assumption of the Moore-Read theory. We measure the electron heating under radio frequency excitation, and show that we are able to detect NMR at electron temperatures down to 30 mK.PACS numbers: 73.43.FjThe physics of interacting electrons at half integer filling factor has intrigued researchers over the past two decades. It was found that the behavior at the first Landau level can be understood in terms of non-interacting composite fermions (CF) at zero magnetic field [1]. Numerous experimental findings confirm this picture, and establish the formation of a non-gaped state at ν = 1/2. The behavior in the second Landau level is, however, fundamentally different. Early experiments, dating back to the late eighties, show the formation of a fractional quantum Hall (FQH) state at ν = 5/2 [2,3]. This observation has challenged the CF theory and triggered an intense theoretical effort. Early on Moore and Read (MR) have suggested that a weak residual attractive interaction in the second Landau level gives rise to pairing of the CFs, and to the formation of a gaped state [4]. One of the exciting aspects of MR theory is the predicted excitation spectrum of the ν = 5/2 state, which should consist of quasiparticles that obey non-Abelian braiding statistics. It was shown that this property may turn the 5/2 state into a platform for quantum computing by means of topological manipulations [5].The examination of MR theory has become the focus of intensive experimental effort in recent years. A major support for its validity has been provided by the measurement of the quasiparticle charge, found to be e/4, in agreement with the prediction of the MR theory [6,7]. However, this finding is also consistent with other competing theories [1], and further experimental support is needed. The determination of the electron spin polarization can provide this needed support. A central assumption of the MR theory is that the electrons in the second Landau level are fully-polarized, and can therefore form pairs with p-type symmetry. Hence, confirming this point would provide a strong experimental evidence for the validity of the MR theory. Unfortunately, the experiments realized so far to probe the polarization at ν = 5/2 have led to ambiguous results: Tilted field experiments have shown that the ν = 5/2 gap decreases with tilt angle [8,9], which could be interpreted in favor of a spin depolarized ground state. However, this behavior may also originate from the destruction of the 5/2 state induced by the orbital coupling to the parallel magnetic field [10][11][12]. Optical measurements also provided indications, which supported an unpolarized ground state. Raman experiments have shown diminishing of the spin flip mode, and were ...

Spin and Charge Ordering in the Quantum Hall Regime

“…For a discussion of the main candidate wavefunctions and a review on the experiments performed so far, we refer to section 2.6.2. In the course of acquiring these results, two similar pieces of work were published by other groups [158,159]. The authors also inferred a spin polarized 5 ⁄2 state in consistence with our findings.…”

“…Fig. 4.6a reveals a well developed 5 ⁄2 state with becoming vanishingly small in contrast to the experimental conditions in references [158,159]. This is an important point since the electron system at = 5 ⁄2 is spin polarized also in the absence of a quantized state.…”

“…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.…”

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…A number of methods [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] were invented and several experiments [29][30][31][32][33][34][35][36][37][38][39][40] were performed in an attempt to determine the right ground state. One approach 39,40 consists in the measurement of the tunneling current through a quantum point contact (QPC) between the edges of a 5/2 FQH liquid.…”