Observation of neutral modes in the fractional quantum Hall regime

Abstract

The quantum Hall effect takes place in a two-dimensional electron gas under a strong magnetic field and involves current flow along the edges of the sample. For some particle–hole conjugate states of the fractional regime (for example, with fillings between 1/2 and 1 of the lowest Landau level), early predictions suggested the presence of counter-propagating edge currents in addition to the expected ones. When this did not agree with the measured conductance, it was suggested that disorder and interactions will lead to counter-propagating modes that carry only energy—the so called neutral modes. In addition, a neutral upstream mode (the Majorana mode) was expected for selected wavefunctions proposed for the even-denominator filling 5/2. Here we report the direct observation of counter-propagating neutral modes for fillings of 2/3, 3/5 and 5/2. The basis of our approach is that, if such modes impinge on a narrow constriction, the neutral quasiparticles will be partly reflected and fragmented into charge carriers, which can be detected through shot noise measurements. We find that the resultant shot noise is proportional to the injected current. Moreover, when we simultaneously inject a charge mode, the presence of the neutral mode was found to significantly affect the Fano factor and the temperature of the backscattered charge mode. In particular, such observations for filling 5/2 may single out the non-Abelian wavefunctions for the state.

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Figure 1: The experimental set-up for measuring the neutral mode.
Figure 2: Detection of the neutral mode at v b = 2/3.
Figure 3: The effect of impinging the neutral mode simultaneously with the charge mode on the QPC constriction at v b = 2/3.
Figure 4: Measurements at fractional state v b = 2/5.
Figure 5: Testing for the existence of the neutral mode at v b = 3/5.
Figure 6: Testing for the existence of the neutral mode at v b = 5/2.

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Acknowledgements

We thank D. Feldman, Y. Gefen, A. Stern and I. Neder for discussions and E. Alcobi for comments on the manuscript. The work received partial support from the Israeli Science Foundation (ISF), the Minerva Foundation, the German Israeli Foundation (GIF), the German Israeli Project Cooperation (DIP), the European Research Council under the European Community's Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement 227716, and the US-Israel Bi-National Science Foundation. N.O. acknowledges support from the Israeli Ministry of Science and Technology. C.L.K. acknowledges support from the NSF (DMR 0906175).

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A.B., N.O., H.I. and M.H. designed the experiment and wrote the paper. A.B., N.O. and H.I. performed the experiment, C.L.K. wrote the paper, V.U. grew the 2DEG and D.H. did the electron beam lithography.

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Correspondence to M. Heiblum.

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The authors declare no competing financial interests.

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Bid, A., Ofek, N., Inoue, H. et al. Observation of neutral modes in the fractional quantum Hall regime. Nature 466, 585–590 (2010). https://doi.org/10.1038/nature09277

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