Letter | Published:

Observed quantization of anyonic heat flow

Nature volume 545, pages 7579 (04 May 2017) | Download Citation


The quantum of thermal conductance of ballistic (collisionless) one-dimensional channels is a unique fundamental constant1. Although the quantization of the electrical conductance of one-dimensional ballistic conductors has long been experimentally established2, demonstrating the quantization of thermal conductance has been challenging as it necessitated an accurate measurement of very small temperature increase. It has been accomplished for weakly interacting systems of phonons3,4, photons5 and electronic Fermi liquids6,7,8; however, it should theoretically also hold in strongly interacting systems, such as those in which the fractional quantum Hall effect is observed. This effect describes the fractionalization of electrons into anyons and chargeless quasiparticles, which in some cases can be Majorana fermions2. Because the bulk is incompressible in the fractional quantum Hall regime, it is not expected to contribute substantially to the thermal conductance, which is instead determined by chiral, one-dimensional edge modes. The thermal conductance thus reflects the topological properties of the fractional quantum Hall electronic system, to which measurements of the electrical conductance give no access9,10,11,12. Here we report measurements of thermal conductance in particle-like (Laughlin–Jain series) states and the more complex (and less studied) hole-like states in a high-mobility two-dimensional electron gas in GaAs–AlGaAs heterostructures. Hole-like states, which have fractional Landau-level fillings of 1/2 to 1, support downstream charged modes as well as upstream neutral modes13, and are expected to have a thermal conductance that is determined by the net chirality of all of their downstream and upstream edge modes. Our results establish the universality of the quantization of thermal conductance for fractionally charged and neutral modes. Measurements of anyonic heat flow provide access to information that is not easily accessible from measurements of conductance.

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  1. 1.

    Quantum limits to the flow of information and entropy. J. Phys. A 16, 2161–2171 (1983)

  2. 2.

    & (eds) Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-dimensional Semiconductor Structures (Wiley, 1996)

  3. 3.

    , , & Measurement of the quantum of thermal conductance. Nature 404, 974–977 (2000)

  4. 4.

    , & Thermal conductance and electron–phonon coupling in mechanically suspended nanostructures. Appl. Phys. Lett. 81, 31–33 (2002)

  5. 5.

    , & Single-mode heat conduction by photons. Nature 444, 187–190 (2006)

  6. 6.

    , , , & Peltier coefficient and thermal conductance of a quantum point contact. Phys. Rev. Lett. 68, 3765–3768 (1992)

  7. 7.

    et al. Quantum thermal conductance of electrons in a one-dimensional wire. Phys. Rev. Lett. 97, 056601 (2006)

  8. 8.

    et al. Quantum limit of heat flow across a single electronic channel. Science 342, 601–604 (2013)

  9. 9.

    & Impurity scattering and transport of fractional quantum Hall edge states. Phys. Rev. B 51, 13449–13466 (1995)

  10. 10.

    & Quantized thermal transport in the fractional quantum Hall effect. Phys. Rev. B 55, 15832–15837 (1997)

  11. 11.

    , & Thermal transport in chiral conformal theories and hierarchical quantum Hall states. Nucl. Phys. B 636, 568–582 (2002)

  12. 12.

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

  13. 13.

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

  14. 14.

    , , , & Upstream neutral modes in the fractional quantum Hall effect regime: heat waves or coherent dipoles. Phys. Rev. Lett. 108, 226801 (2012)

  15. 15.

    , , , & Extracting net current from an upstream neutral mode in the fractional quantum Hall regime. Nat. Commun. 3, 1289 (2012)

  16. 16.

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

  17. 17.

    , & Hot-electron effects in metals. Phys. Rev. B 49, 5942–5955 (1994)

  18. 18.

    Composite Fermions (Cambridge Univ. Press, 2007)

  19. 19.

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

  20. 20.

    et al. A new paradigm for edge reconstruction in fractional quantum Hall states. Nat. Phys. 13, 4010–4016 (2017)

  21. 21.

    , , , & Shot noise and charge at the 2/3 composite fractional quantum Hall state. Phys. Rev. Lett. 103, 236802 (2009)

  22. 22.

    , & Equilibration of quantum Hall edge states by an Ohmic contact. Phys. Rev. B 88, 165307 (2013)

  23. 23.

    Cryogenic scanning force microscopy of quantum Hall samples: adiabatic transport originating in anisotropic depletion at contact interfaces. Phys. Rev. B 82, 121305 (2010)

  24. 24.

    , , & Scattering of a two-dimensional electron gas by a correlated system of ionized donors. Semicond. Sci. Technol. 9, 2031–2041 (1994)

  25. 25.

    , & Correlated charged donors and strong mobility enhancement in a two-dimensional electron gas. Phys. Rev. B 49, 14790(R)–14793(R) (1994)

  26. 26.

    & Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge. Phys. Rev. B 33, 551–558 (1986)

  27. 27.

    & Linear and nonlinear mesoscopic thermoelectric transport with coupling to heat bath. C. R. Phys. 17, 1047–1059 (2016)

  28. 28.

    & Suppression of shot noise in metallic diffusive conductors. Phys. Rev. B 46, 1889–1892 (1992)

  29. 29.

    & Semiclassical theory of conductance and noise in open chaotic cavities. Phys. Rev. Lett. 84, 1280–1283 (2000)

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We acknowledge the help and advice of R. Sabo, I. Gurman, N. OfeK, H.-K. Choi and D. Mahalu. M.H. acknowledges the European Research Council under the European Community’s Seventh Framework Programme, grant agreement number 339070, the partial support of the Minerva Foundation, grant number 711752, and, together with V.U., the German Israeli Foundation (GIF), grant number I-1241-303.10/2014, and the Israeli Science Foundation (ISF). A.S. and Y.O. acknowledge the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC, grant agreement number 339070, and the Israeli Science Foundation, ISF agreement number 13335/16. Y.O. acknowledges CRC 183 of the DFG. D.E.F. acknowledges support by the NSF under grant number DMR-1205715.

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  1. Braun Center for Sub-Micron Research, Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

    • Mitali Banerjee
    • , Moty Heiblum
    • , Amir Rosenblatt
    • , Yuval Oreg
    • , Ady Stern
    •  & Vladimir Umansky
  2. Department of Physics, Brown University, Providence, Rhode Island 02912, USA

    • Dima E. Feldman


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M.B., A.R. and M.H. designed the experiment. M.B. and A.R. fabricated the devices with input from M.H. A.R. participated in initial measurements. M.B. and M.H. preformed the measurements, did the analysis and guided the experimental work. Y.O., D.E.F. and A.S. worked on the theoretical aspects. V.U. grew the heterostructures in which the two-dimensional electron gas (2DEG) is embedded. All authors contributed to writing the manuscript.

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The authors declare no competing financial interests.

Corresponding author

Correspondence to Moty Heiblum.

Reviewer Information Nature thanks G. Gervais and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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