Introduction and Motivation: from Helical Modes to Topological Quantum Computing

  • Yonatan CohenEmail author
Part of the Springer Theses book series (Springer Theses)


In recent years, great interest has been sparked in the condensed matter physics community due to the possibility of engineering exotic quantum states called Majorana zero modes (MZMs).


  1. 1.
    Wilczek, F.: Majorana returns. Nat. Phys. 5, 614–618 (2009)CrossRefGoogle Scholar
  2. 2.
    Majorana, E.: Teoria simmetrica dell’elettrone e del positrone. Nuovo. Cim. 14, 171–184 (1937)ADSCrossRefGoogle Scholar
  3. 3.
    Ivanov, D.A.: Non-Abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Alicea, J., Oreg, Y., Refael, G., von Oppen, F., Fisher, M.P.A.: Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412–417 (2011)CrossRefGoogle Scholar
  5. 5.
    Lee, E.J.H., et al.: Spin-resolved Andreev levels and parity crossings in hybrid superconductor–semiconductor nanostructures. Nat. Nanotechnol. 9, 79–84 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    Moore, G., Read, N.: Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Das Sarma, S., Nayak, C., Tewari, S.: Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: non-Abelian braiding statistics of vortices in a px + ipy superconductor. Phys. Rev. B 73, 220502 (2006)CrossRefGoogle Scholar
  8. 8.
    Kitaev, A.Y.: Unpaired Majorana fermions in quantum wires. Phys. Usp. 44, 131–136 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    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)ADSCrossRefGoogle Scholar
  10. 10.
    Oreg, Y., Refael, G., Von Oppen, F.: Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    Nilsson, J., Akhmerov, A.R., Beenakker, C.W.J.: Splitting of a Cooper Pair by a pair of Majorana bound states. Phys. Rev. Lett. 101, 120403 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Read, N., Green, D.: Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267–10297 (2000)ADSCrossRefGoogle Scholar
  13. 13.
    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)ADSCrossRefGoogle Scholar
  14. 14.
    Bid, A., et al.: Observation of neutral modes in the fractional quantum Hall effect regime. In AIP Conference Proceedings, 1399, 633–634 (2011)Google Scholar
  15. 15.
    Willett, R.L., Pfeiffer, L.N., West, K.W.: Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations. Proc. Natl. Acad. Sci. U. S. A. 106, 8853–8858 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    Banerjee, M., et al.: Observation of half-integer thermal Hall conductance arXiv:1710.00492 (2017)
  17. 17.
    Fu, L., Kane, C.L.: Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 96407 (2008)ADSCrossRefGoogle Scholar
  18. 18.
    Potter, A.C., Lee, P.A.: Engineering a p+ ip superconductor: comparison of topological insulator and Rashba spin-orbit-coupled materials. Phys. Rev. B 83 (2011)Google Scholar
  19. 19.
    Hutter, A., Loss, D.: Quantum computing with parafermions. Phys. Rev. B 93, 125105 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    Alicea, J., Fendley, P.: Topological phases with parafermions: theory and blueprints. Annu. Rev. Condens. Matter Phys. 7, 119–139 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Clarke, D.J., Alicea, J., Shtengel, K.: Exotic non-abelian anyons from conventional fractional quantum Hall states. Nat. Commun. 4, 1348 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    Bernevig, B.A., Hughes, T.L., Zhang, S.-C.: Quantum spin hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    Knez, I., Du, R.-R., Sullivan, G.: Evidence for helical edge modes in inverted InAs/ GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    Bocquillon, E., et al.: Gapless Andreev bound states in the quantum spin Hall insulator HgTe. Nat. Nanotechnol. 12, 137–143 (2016)ADSCrossRefGoogle Scholar
  25. 25.
    Hart, S., et al.: Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014)CrossRefGoogle Scholar
  26. 26.
    Deacon, R.S., et al.: Josephson radiation from gapless Andreev bound states in HgTe-based topological junctions. Phys. Rev. X 7, 21011 (2017)Google Scholar
  27. 27.
    Oreg, Y., Sela, E., Stern, A.: Fractional helical liquids in quantum wires. Phys. Rev. B 89, 115402 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Klinovaja, J., Loss, D.: Time-reversal invariant parafermions in interacting Rashba nanowires. Phys. Rev. B 90, 45118 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    Klinovaja, J., Loss, D.: Parafermions in an interacting nanowire bundle. Phys. Rev. Lett. 112, 246403 (2014)ADSCrossRefGoogle Scholar
  30. 30.
    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)ADSCrossRefGoogle Scholar
  31. 31.
    Wan, Z., et al.: Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures. Nat. Commun. 6, 7426 (2015)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Braun Center for Submicron ResearchWeizmann Institute of ScienceRehovotIsrael

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