Robust integer and fractional helical modes in the quantum Hall effect

Abstract

Electronic systems harboring one-dimensional helical modes, where spin and momentum are locked, have lately become an important field of their own. When coupled to a conventional superconductor, such systems are expected to manifest topological superconductivity; a unique phase hosting exotic Majorana zero modes. Even more interesting are fractional helical modes, yet to be observed, which open the route for realizing generalized parafermions. Possessing non-Abelian exchange statistics, these quasiparticles may serve as building blocks in topological quantum computing. Here, we present a new approach to form protected one-dimensional helical edge modes in the quantum Hall regime. The novel platform is based on a carefully designed double-quantum-well structure in a GaAs-based system hosting two electronic sub-bands; each tuned to the quantum Hall effect regime. By electrostatic gating of different areas of the structure, counter-propagating integer, as well as fractional, edge modes with opposite spins are formed. We demonstrate that, due to spin protection, these helical modes remain ballistic over large distances. In addition to the formation of helical modes, this platform can serve as a rich playground for artificial induction of compounded fractional edge modes, and for construction of edge-mode-based interferometers.

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Fig. 1: Schematic illustration of the concept of creating helical edge modes in a double-layer QHE system.
Fig. 2: MBE growth sequence, lithographic patterning and actual fan diagram.
Fig. 3: Tuning the structure to host integer helical modes.
Fig. 4: Spin-protected intermode tunnelling.
Fig. 5: Formation of fractional helical states.
Fig. 6: Contacting the helical edge modes directly.

References

  1. 1.

    Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys. Usp. 44, 131–136 (2001).

  2. 2.

    Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

  3. 3.

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 96407 (2008).

  4. 4.

    Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 76501 (2012).

  5. 5.

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

  6. 6.

    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. Nat. Phys. 8, 795–799 (2012).

  7. 7.

    Deng, M. T. et al. Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device. Nano Lett. 12, 6414–6419 (2012).

  8. 8.

    Churchill, H. O. H. et al. Superconductor-nanowire devices from tunneling to the multichannel regime: zero-bias oscillations and magnetoconductance crossover. Phys. Rev. B 87, 241401 (2013).

  9. 9.

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

  10. 10.

    Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

  11. 11.

    Karzig, T. et al. Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes. Phys. Rev. B 95, 235305 (2017).

  12. 12.

    Das Sarma, S., Freedman, M. & Nayak, C. Majorana zero modes and topological quantum computation. NPJ Quant. Inf. 1, 15001 (2015).

  13. 13.

    Clarke, D. J., Sau, J. D. & Das Sarma, S. A practical phase gate for producing bell violations in Majorana wires. Phys. Rev. X 6, 21005 (2016).

  14. 14.

    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).

  15. 15.

    Cheng, Q. B., He, J. & Kou, S. P. Verifying non-Abelian statistics by numerical braiding Majorana fermions. Phys. Lett. A 380, 779–782 (2016).

  16. 16.

    Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 77001 (2010).

  17. 17.

    Oreg, Y., Refael, G. & Von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).

  18. 18.

    Vaezi, A. Superconducting analogue of the parafermion fractional quantum Hall states. Phys. Rev. X 4, 31009 (2014).

  19. 19.

    Clarke, D. J., Alicea, J. & Shtengel, K. Exotic non-Abelian anyons from conventional fractional quantum Hall states. Nat. Commun. 4, 1348 (2013).

  20. 20.

    Lindner, N. H., Berg, E., Refael, G. & Stern, A. Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states. Phys. Rev. X 2, 41002 (2012).

  21. 21.

    König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

  22. 22.

    Knez, I. et al. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011).

  23. 23.

    Hart, S. et al. Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014).

  24. 24.

    Heedt, S. et al. Signatures of interaction-induced helical gaps in nanowire quantum point contacts. Nat. Phys. 13, 563–567 (2017).

  25. 25.

    Kammhuber, J. et al. Conductance through a helical state in an indium antimonide nanowire. Nat. Commun. 8, 478 (2017).

  26. 26.

    Sanchez-Yamagishi, J. D. et al. Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer. Nat. Nanotechnol. 12, 118–122 (2016).

  27. 27.

    Kazakov, A. et al. Electrostatic control of quantum Hall ferromagnetic transition: a step toward reconfigurable network of helical channels. Phys. Rev. B 94, 75309 (2016).

  28. 28.

    Haug, R. J. et al. Quantized multichannel magnetotransport through a barrier in two dimensions. Phys. Rev. Lett. 61, 2797 (1988).

  29. 29.

    Nuebler, J. et al. Quantized ν = 5/2 state in a two-subband quantum Hall system. Phys. Rev. Lett. 108, 46804 (2012).

  30. 30.

    Liu, Y. et al. Evolution of the 7/2 fractional quantum Hall state in two-subband systems. Phys. Rev. Lett. 107, 266802 (2011).

  31. 31.

    Barkeshli, M. & Qi, X. L. Synthetic topological qubits in conventional bilayer quantum Hall systems. Phys. Rev. X 4, 41035 (2014).

  32. 32.

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

  33. 33.

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

  34. 34.

    Grivnin, A. et al. Nonequilibrated counterpropagating edge modes in the fractional quantum Hall regime. Phys. Rev. Lett. 113, 266803 (2014).

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Acknowledgements

We acknowledge Johannes Nübler, Erez Berg, Yuval Oreg, Ady Stern,Yuval Gefen, Jinhong Park, Dmitri Feldman, Kyrylo Snizhko and Onder Gul for fruitful discussions. We thank Diana Mahalu for the e-beam processing and Vitaly Hanin for the help in the ALD process. M.H. acknowledges the partial support of the Israeli Science Foundation (ISF), the Minerva foundation, the US–Israel Bi-National Science Foundation (BSF), the European Research Council under the European Community’s Seventh Framework Program (FP7/2007–2013)/ERC Grant agreement 339070 and the German–Israeli Project Cooperation (DIP).

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Author information

Y.C. and Y.R. contributed equally to this work in heterostructure design, sample design, device fabrication, measurement set-up, data acquisition, data analysis and interpretation, and writing of the paper. D.B. contributed in heterostructure simulation, data analysis and interpretation, and writing of the paper. M.H. contributed in heterostructure design, sample design, data interpretation and writing of the paper. V.U. contributed in heterostructure design and molecular beam epitaxy growth.

Correspondence to Moty Heiblum.

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Ronen, Y., Cohen, Y., Banitt, D. et al. Robust integer and fractional helical modes in the quantum Hall effect. Nature Phys 14, 411–416 (2018). https://doi.org/10.1038/s41567-017-0035-2

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