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Shot noise does not always provide the quasiparticle charge

Nature Physics volume 18, pages 1476–1481 (2022)Cite this article

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Abstract

The fractional charge of quasiparticles is a fundamental feature of quantum Hall effect states. The charge—important in characterizing the state and in interference experiments—has long been measured via shot noise at moderate temperatures, with the Fano factor revealing the charge of the quasiparticles. However, at sufficiently low temperatures of ~10 mK, we previously found that the Fano factor is instead equal to the bulk filling factor. Noise with this pattern was also observed on intermediate conductance plateaux in the transmission of the quantum point contact, where shot noise is not expected. Here, we extend this low-temperature behaviour of the Fano factor to a situation where the edge modes do not sit at the physical edge of the device but instead reside in an artificially constructed interface at the boundary between two adjoining quantum Hall effect states: the tested state and a different state. We attribute the unexpected shot noise behaviour to upstream neutral modes that proliferate at the lowest spinless Landau level. We present a theoretical approach based on an interplay between charge and neutral modes that hints at the origin of the universal Fano factor.

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Fig. 1: Interface edge modes.
Fig. 2: Experimental set-up for shot noise measurement with interface modes.
Fig. 3: Shot noise with two types of interface 2/3 mode (1 − 1/3 and 2/3 − 0).
Fig. 4: Theoretical model with the example of reconstructed v = 1/3.

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Data related to this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

  1. Laughlin, R. B. Anomalous quantum Hall effect—an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).

    Article  ADS  Google Scholar 

  2. Heiblum, M. Quantum shot noise in edge channels. Phys. Status Solidi B Basic Solid State Phys. 243, 3604–3616 (2006).

    Article  ADS  Google Scholar 

  3. Ronen, Y. et al. Charge of a quasiparticle in a superconductor. Proc. Natl Acad. Sci. USA 113, 1743–1748 (2016).

    Article  ADS  Google Scholar 

  4. Jehl, X., Sanquer, M., Calemczuk, R. & Mailly, D. Detection of doubled shot noise in short normal-metal/superconductor junctions. Nature 405, 50–53 (2000).

    Article  ADS  Google Scholar 

  5. Bastiaans, K. M. et al. Direct evidence for Cooper pairing without a spectral gap in a disordered superconductor above Tc. Science 374, 608–611 (2021).

    Article  ADS  Google Scholar 

  6. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2019).

    Article  ADS  Google Scholar 

  7. Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).

    Article  ADS  Google Scholar 

  8. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  Google Scholar 

  9. Prange, R. & Girvin, S. M. The Quantum Hall Effect (Springer, 1990).

  10. Sarma, S. D. & Pinczuk, A. Perspective in Quantum Hall Effects (Wiley, 1996).

  11. Halperin, B. I. & Jain, J. K. Fractional Quantum Hall Effects: New Developments (World Scientific, 2020).

  12. Halperin, B. I. Quantized Hall conductance, current-carrying edge states, and the existence of extended states in a two-dimensional disordered potential. Phys. Rev. B 25, 2185–2190 (1982).

    Article  ADS  Google Scholar 

  13. Wen, X.-G. Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons (Oxford Univ. Press, 2004).

  14. Kane, C. L. & Fisher, M. P. A. in Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low‐Dimensional Semiconductor Structures (eds Das Sarma, S. & Pinczuk, A.) Ch. 4 (Wiley, 1996).

  15. Wen, X. G. Gapless boundary excitations in the quantum Hall states and in the chiral spin states. Phys. Rev. B 43, 11025–11036 (1991).

    Article  ADS  Google Scholar 

  16. Stern, A. Anyons and the quantum Hall effect—a pedagogical review. Ann. Phys. 323, 204–249 (2008).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Zheng, H. Z., Wei, H. P., Tsui, D. C. & Weimann, G. Gate-controlled transport in narrow GaAs/AlxGa1 − xAs heterostructures. Phys. Rev. B 34, 5635–5638 (1986).

    Article  ADS  Google Scholar 

  18. Heiblum, M. & Feldman, D. E. Edge probes of topological order. Int. J. Mod. Phys. A 35, 2030009 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  19. Chang, A. M. Chiral Luttinger liquids at the fractional quantum Hall edge. Rev. Mod. Phys. 75, 1449–1505 (2003).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  20. dePicciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).

    Article  ADS  Google Scholar 

  21. Saminadayar, L., Glattli, D. C., Jin, Y. & Etienne, B. Observation of the e/3 fractionally charged Laughlin quasiparticle. Phys. Rev. Lett. 79, 2526–2529 (1997).

    Article  ADS  Google Scholar 

  22. Reznikov, M., de Picciotto, R., Griffiths, T. G., Heiblum, M. & Umansky, V. Observation of quasiparticles with one-fifth of an electron’s charge. Nature 399, 238–241 (1999).

    Article  ADS  Google Scholar 

  23. Dolev, M., Heiblum, M., Umansky, V., Stern, A. & Mahalu, D. Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state. Nature 452, 829–834 (2008).

    Article  ADS  Google Scholar 

  24. Chung, Y. C., Heiblum, M. & Umansky, V. Scattering of bunched fractionally charged quasiparticles. Phys. Rev. Lett. 91, 216804 (2003).

    Article  ADS  Google Scholar 

  25. Bid, A., Ofek, N., Heiblum, M., Umansky, V. & Mahalu, D. Shot noise and charge at the 2/3 composite fractional quantum Hall state. Phys. Rev. Lett. 103, 236802 (2009).

    Article  ADS  Google Scholar 

  26. Bhattacharyya, R., Banerjee, M., Heiblum, M., Mahalu, D. & Umansky, V. Melting of interference in the fractional quantum Hall effect: appearance of neutral modes. Phys. Rev. Lett. 122, 246801 (2019).

    Article  ADS  Google Scholar 

  27. Bid, A. et al. Observation of neutral modes in the fractional quantum Hall regime. Nature 466, 585–590 (2010).

    Article  ADS  Google Scholar 

  28. Inoue, H. et al. Proliferation of neutral modes in fractional quantum Hall states. Nat. Commun. 5, 4067 (2014).

    Article  ADS  Google Scholar 

  29. Wang, J., Meir, Y. & Gefen, Y. Edge reconstruction in the ν = 2/3 fractional quantum Hall state. Phys. Rev. Lett. 111, 246803 (2013).

    Article  ADS  Google Scholar 

  30. Khanna, U., Goldstein, M. & Gefen, Y. Edge reconstruction and emergent neutral modes in integer and fractional quantum Hall phases. Low Temp. Phys. 48, 420–427 (2022).

    Article  ADS  Google Scholar 

  31. Meir, Y. Composite edge states in the ν = 2/3 fractional quantum Hall regime. Phys. Rev. Lett. 72, 2624–2627 (1994).

    Article  ADS  Google Scholar 

  32. Hu, L. & Zhu, W. Abelian origin of ν = 2/3 and 2 + 2/3 fractional quantum Hall effect. Phys. Rev. B 105, 165415 (2022).

    Article  Google Scholar 

  33. Khanna, U., Goldstein, M. & Gefen, Y. Fractional edge reconstruction in integer quantum Hall phases. Phys. Rev. B 103, L121302 (2021).

    Article  ADS  Google Scholar 

  34. Sabo, R. et al. Edge reconstruction in fractional quantum Hall states. Nat. Phys. 13, 491–496 (2017).

    Article  Google Scholar 

  35. Kane, C. L., Fisher, M. P. & Polchinski, J. Randomness at the edge: theory of quantum Hall transport at filling ν = 2/3. Phys. Rev. Lett. 72, 4129–4132 (1994).

    Article  ADS  Google Scholar 

  36. Spånslätt, C., Park, J., Gefen, Y. & Mirlin, A. D. Conductance plateaus and shot noise in fractional quantum Hall point contacts. Phys. Rev. B 101, 075308 (2020).

    Article  ADS  Google Scholar 

  37. Lin, C. et al. Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device. Phys. Rev. B 99, 195304 (2019).

    Article  ADS  Google Scholar 

  38. Martin, T. & Landauer, R. Wave-packet approach to noise in multichannel mesoscopic systems. Phys. Rev. B 45, 1742–1755 (1992).

    Article  ADS  Google Scholar 

  39. Buttiker, M. Scattering theory of current and intensity noise correlations in conductors and wave guides. Phys. Rev. B 46, 12485–12507 (1992).

    Article  ADS  Google Scholar 

  40. Feldman, D. E. & Heiblum, M. Why a noninteracting model works for shot noise in fractional charge experiments. Phys. Rev. B 95, 115308 (2017).

    Article  ADS  Google Scholar 

  41. Dolev, M. et al. Dependence of the tunneling quasiparticle charge determined via shot noise measurements on the tunneling barrier and energetics. Phys. Rev. B 81, 161303 (2010).

    Article  ADS  Google Scholar 

  42. Comforti, E., Chung, Y. C., Heiblum, M., Umansky, V. & Mahalu, D. Bunching of fractionally charged quasiparticles tunnelling through high-potential barriers. Nature 416, 515–518 (2002).

    Article  ADS  Google Scholar 

  43. Chamon, C. & Wen, X. G. Sharp and smooth boundaries of quantum Hall liquids. Phys. Rev. B 49, 8227–8241 (1994).

    Article  ADS  Google Scholar 

  44. Khanna, U., Murthy, G., Rao, S. & Gefen, Y. Spin mode switching at the edge of a quantum Hall system. Phys. Rev. Lett. 119, 186804 (2017).

    Article  ADS  Google Scholar 

  45. Park, J., Rosenow, B. & Gefen, Y. Symmetry-related transport on a fractional quantum Hall edge. Phys. Rev. Res. 3, 023083 (2021).

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with I. Gornyi. In particular, we are indebted to A. Mirlin for pointing out the difficulty with our assumption of independent pulses arriving at the drain. We acknowledge the continuous support of the Sub-Micron Center staff. M.H. acknowledges support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013)/ERC under grant agreement no. 713351, partial support of the Minerva Foundation with funding from the Federal German Ministry for Education and Research (grant no. 713534). M.G. was supported by the Israel Science Foundation and the Directorate for Defense Research and Development grant no. 3427/21 and by the US–Israel Binational Science Foundation (grants nos. 2016224 and 2020072). Y.G. was supported by CRC 183 (project C01), the Minerva Foundation, DFG grant no. RO 2247/11-1, MI 658/10-2, the German–Israeli Foundation (grant no. I-118-303.1-2018), the National Science Foundation (award DMR- 2037654) and the US–Israel Binational Science Foundation, and the Helmholtz International Fellow Award. A.D. was supported by the German–Israeli Foundation (grant no. I-1505-303.10/2019). A.D. also thanks the Koshland Foundation for a Koshland Fellowship, the Israel Planning and Budgeting Committee and Weizmann Institute of Science, Israel Dean of Faculty fellowship for financial support.

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Author notes

  1. Rajarshi Bhattacharyya

    Present address: Department of Physics, University of California, San Diego, La Jolla, CA, USA

Authors and Affiliations

  1. Braun Center for Submicron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Sourav Biswas, Rajarshi Bhattacharyya, Hemanta Kumar Kundu, Moty Heiblum & Vladimir Umansky

  2. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, Israel

    Ankur Das & Yuval Gefen

  3. Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel Aviv, Israel

    Moshe Goldstein

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Contributions

S.B. and R.B. fabricated the devices, performed the measurements and analysed the data with H.K.K. M.H. supervised the experiment and the analysis. Y.G. contributed to conceiving the theoretical model. A.D., M.G. and Y.G. developed the theoretical model. V.U. grew the GaAs heterostructures. All authors contributed to the writing of the manuscript.

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Correspondence to Moty Heiblum.

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Extended data

Extended Data Fig. 1 Shot noise at integer bulk vb = 1 with symmetric and asymmetric QPC.

a, Downstream current noise (Si) at bulk filling factor vb = 1 for the regular case, that is, when both the upper and lower modes are \(\nu _{{{{\mathrm{int}}}}}^{{{{\mathrm{l}}}},{{{\mathrm{u}}}}} = 1\). Fano factor is F = 0.93. b, Si when the partitioned edge is \(1_{{{\mathrm{b}}}} - 2/3_{{{\mathrm{g}}}} = 1/3_{{{{\mathrm{int}}}}}\), and the QPC is asymmetric with \(\nu _{{{\mathrm{g}}}}^{{{\mathrm{l}}}} \ne \nu _{{{\mathrm{g}}}}^{{{\mathrm{u}}}}\) and \(\nu _{{{\mathrm{g}}}}^{{{\mathrm{u}}}}\) not quantized. Obtained F = 1, with an accuracy of ±0.05. The electron temperature is slightly higher (about 3–4 mK) than the fridges’ base temperature.

Source data

Extended Data Fig. 2 QPC transmission for two types of interface 2/3 modes: 1 − 1/3 and 2/3 − 0.

QPC transmission as a function of upper-gate voltage \(V_{{{\mathrm{g}}}}^u\) when the incoming mode at the lower bulk-gate interface is 1b − 1/3g = 2/3int (left) and 2/3b − 0g = 2/3int (right). The transmission shows a plateau at t = 1/2 for both cases, indicating edge reconstruction.

Source data

Extended Data Fig. 3 Quasiparticle bunching at strong backscattering of 2/3 − 0 edge mode.

Quasiparticle bunching leads to electron tunneling with F ≅ 1 at low QPC transmission and small impinging bias current (red plots). At a higher bias current, the transmission increases and the Fano factor becomes close to 2/3. This is consistent with the result of 2/3 edge in a regular QPC (Ref. 25). For the comparison, shot noise with F ≅ 2/3 at a higher transmission over the full bias current range is also shown (blue plots).

Source data

Extended Data Fig. 4 Upstream noise and Fano factor for newly engineered fractional states 2/3 − 1/3 = 1/3 and 2/3 − 4/15 = 2/5.

a,b, Spectral density of upstream current noise, measured at an upstream amplifier 70 µm distant from the source hot-spot. Unlike ubiquitous 1/3 and 2/5 modes, the interface 2/3b − 1/3g = 1/3int and 2/3b − 4/15g = 2/5int modes are expected to have negative or zero thermal conductance (Kxy); hence, they carry topological neutral modes. Note that 4/15 is a new quantum Hall state, which we could stabilize only by gating in a few bulk-gate devices. c,d, Spectral density of downstream current noise for 1/3int at t ≈ 0.63 and for 2/5int at t ≈ 0.56 when the QPC is set at symmetric configuration. Blue dots are the measured data and black solid lines are the fit. Estimated Fano factors are close to 2/3, the bulk filling factor. Schematics in the respective inset describe the interface mode incident on the QPC and the corresponding bulks.

Source data

Supplementary information

Supplementary Information

Supplementary Sections I–V, Figs. 1–15 and Discussion.

Source data

Source Data Fig. 1

Statistical source data for Fig. 1b

Source Data Fig. 2

Statistical source data for Fig. 2b–d

Source Data Fig. 3

Statistical source data for Fig. 3a,b

Source Data Extended Data Fig. 1

Statistical source data for Extended Data Fig. 1a,b

Source Data Extended Data Fig. 2

Statistical source data for Extended Data Fig. 2

Source Data Extended Data Fig. 3

Statistical source data for Extended Data Fig. 3

Source Data Extended Data Fig. 4

Statistical source data for Extended Data Fig. 4a–d

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Biswas, S., Bhattacharyya, R., Kundu, H.K. et al. Shot noise does not always provide the quasiparticle charge. Nat. Phys. 18, 1476–1481 (2022). https://doi.org/10.1038/s41567-022-01758-x

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