Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment


A quantum phase transition is an abrupt change between two distinct ground states of a many-body system, driven by an external parameter. In the vicinity of the quantum critical point (QCP) where the transition occurs, a new phase may emerge that is determined by quantum fluctuations and is very different from either phase. In particular, a conducting system may exhibit non-Fermi-liquid behaviour. Although this scenario is well established theoretically, controllable experimental realizations are rare. Here, we experimentally investigate the nature of the QCP in a simple nanoscale system—a spin-polarized resonant level coupled to dissipative contacts. We fine-tune the system to the QCP, realized exactly on-resonance and when the coupling between the level and the two contacts is symmetric. Several anomalous transport scaling laws are demonstrated, including a striking non-Fermi-liquid scattering rate at the QCP, indicating fractionalization of the resonant level into two Majorana quasiparticles.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Sample and schematic.
Figure 2: Differential conductance maps close to the QCP.
Figure 3: Critical flow.
Figure 4: Runaway flow.


  1. Sachdev, S. Quantum Phase Transitions 2nd edn (Cambridge Univ. Press, 2011).

    Book  Google Scholar 

  2. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulators with ultracold quantum gases. Nature Phys. 8, 267–276 (2012).

    Article  ADS  Google Scholar 

  3. Potok, R. M., Rau, I. G., Shtrikman, H., Oreg, Y. & Goldhaber-Gordon, D. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007).

    Article  ADS  Google Scholar 

  4. Roch, N., Florens, S., Bouchiat, V., Wernsdorfer, W. & Balestro, F. Quantum phase transition in a single-molecule quantum dot. Nature 453, 633–637 (2008).

    Article  ADS  Google Scholar 

  5. Cubrovic, M., Zaanen, J. & Schalm, K. String theory, quantum phase transitions and the emergent Fermi-liquid. Science 325, 439–444 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  6. Zurek, W. H., Dorner, U. & Zoller, P. Dynamics of a quantum phase transition. Phys. Rev. Lett. 95, 105701 (2005).

    Article  ADS  Google Scholar 

  7. Chung, C-H., Le Hur, K., Vojta, M. & Wölfle, P. Non-equilibrium transport at a dissipative quantum phase transition. Phys. Rev. Lett. 102, 216803 (2009).

    Article  ADS  Google Scholar 

  8. Bomze, Yu., Mebrahtu, H., Borzenets, I., Makarovski, A. & Finkelstein, G. Resonant tunneling in a dissipative environment. Phys. Rev. B 79, 241402(R) (2009).

    Article  ADS  Google Scholar 

  9. Mebrahtu, H. T. et al. Quantum phase transition in a resonant level coupled to interacting leads. Nature 488, 61–64 (2012).

    Article  ADS  Google Scholar 

  10. Wilczek, F. Majorana returns. Nature Phys. 5, 614–618 (2009).

    Article  ADS  Google Scholar 

  11. Avignone, F. T., Elliott, S. R. & Engel, J. Double beta decay, Majorana neutrinos, and neutrino mass. Rev. Mod. Phys. 80, 481–516 (2008).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    Article  ADS  Google Scholar 

  14. Rokhinson, L. P., Liu, X. & Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles. Nature Phys. 8, 795–799 (2012).

    Article  ADS  Google Scholar 

  15. Das, A. et al. Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions. Nature Phys. 8, 887–895 (2012).

    Article  ADS  Google Scholar 

  16. Giamarchi, T. Quantum Physics in One Dimension (Oxford Univ. Press, 2004).

    MATH  Google Scholar 

  17. Emery, V. J. & Kivelson, S. Mapping of the two-channel Kondo problem to a resonant-level model. Phys. Rev. B 46, 10812–10817 (1992).

    Article  ADS  Google Scholar 

  18. Ingold, G-L. & Nazarov, Yu. V. in Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures (eds Grabert, H. & Devoret, M. H.) 21–107 (Plenum Press, 1992).

    Book  Google Scholar 

  19. Safi, I. & Saleur, H. One-channel conductor in an ohmic environment: Mapping to a Tomonaga-Luttinger liquid and full counting statistics. Phys. Rev. Lett. 93, 126602 (2004).

    Article  ADS  Google Scholar 

  20. Jezouin, S. et al. Tomonaga-Luttinger physics in electronic quantum circuits. Nature Commun. 4, 1–8 (2013).

    Article  Google Scholar 

  21. Eggert, S. & Affleck, I. Magnetic impurities in half-integer-spin Heisenberg antiferromagnetic chains. Phys. Rev. B 46, 10866–10883 (1992).

    Article  ADS  Google Scholar 

  22. Meden, V., Enss, T., Andergassen, S., Metzner, W. & Schönhammer, K. Correlation effects on resonant tunneling in one-dimensional quantum wires. Phys. Rev. B 71, 041302(R) (2005).

    Article  ADS  Google Scholar 

  23. Komnik, A. & Gogolin, A. O. Resonant Tunneling between Luttinger liquids: A solvable case. Phys. Rev. Lett. 90, 246403 (2003).

    Article  ADS  Google Scholar 

  24. Sengupta, A. M. & Georges, A. Emery-Kivelson solution of the two-channel Kondo problem. Phys. Rev. B 49, 10020–10022 (1994).

    Article  ADS  Google Scholar 

  25. Coleman, P., Ioffe, L. B. & Tsvelik, A. M. Simple formulation of the two-channel Kondo model. Phys. Rev. B 52, 6611–6627 (1995).

    Article  ADS  Google Scholar 

  26. Zitko, R. Detection of Majorana edge states in topological superconductors through non-Fermi-liquid effects induced in an interacting quantum dot. Phys. Rev. B 83, 195137 (2011).

    Article  ADS  Google Scholar 

  27. Zheng, W., Friedman, J. R., Averin, D. V., Han, S. Y. & Lukens, J. E. Observation of strong Coulomb blockade in resistively isolated tunnel junctions. Solid State Commun. 108, 839–843 (1998).

    Article  ADS  Google Scholar 

  28. Kane, C. L. & Fisher, M. P. A. Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas. Phys. Rev. B 46, 15233–15262 (1992).

    Article  ADS  Google Scholar 

  29. Furusaki, A. & Nagaosa, N. Resonant tunneling in a Luttinger liquid. Phys. Rev. B 47, 3827–3831 (1993).

    Article  ADS  Google Scholar 

  30. Nazarov, Yu. V. & Glazman, L. I. Resonant tunneling of interacting electrons in a one-dimensional wire. Phys. Rev. Lett. 91, 126804 (2003).

    Article  ADS  Google Scholar 

  31. Polyakov, D. G. & Gornyi, I. V. Transport of interacting electrons through a double barrier in quantum wires. Phys. Rev. B 68, 035421 (2003).

    Article  ADS  Google Scholar 

  32. Aristov, D. N. & Wölfle, P. Transport of interacting electrons through a potential barrier: Nonperturbative RG approach. Europhys. Lett. 82, 1–6 (2008).

    Article  Google Scholar 

  33. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    Article  ADS  MathSciNet  Google Scholar 

Download references


We appreciate valuable discussions with I. Affleck, C. H. Chung, P. Coleman, K. Ingersent, K. Le Hur and P. A. Lee. We thank J. Liu for providing the nanotube growth facilities and W. Zhou for helping to optimize the nanotube synthesis. H.Z., S.F. and H.U.B. thank the Fondation Nanosciences de Grenoble for facilitating the exchange between Grenoble and Duke. The work in the US was supported by US DOE awards DE-SC0002765, DE-SC0005237 and DE-FG02-02ER15354.

Author information

Authors and Affiliations



H.T.M., I.V.B. and G.F. designed the experiment. H.T.M. fabricated the samples. H.T.M., I.V.B., Y.V.B., A.I.S. and G.F. conducted the experiment. H.T.M., H.Z., S.F., H.U.B. and G.F. analysed and interpreted the data. H.Z., S.F. and H.U.B. developed the theory.

Corresponding author

Correspondence to G. Finkelstein.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 577 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mebrahtu, H., Borzenets, I., Zheng, H. et al. Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment. Nature Phys 9, 732–737 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing