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In search of Majorana

Abstract

Majorana particles are the same as their antiparticle, and their analogues in condensed matter may be a platform for quantum computing. Here I describe the search for these modes in semiconductor heterostructures and how disorder is a limiting factor.

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Fig. 1: Theoretical predictions for experimental signatures of MZMs.
Fig. 2: Excitation spectra in the topological and trivial regimes.
Fig. 3: The role of disorder in nanowire experiments.

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References

  1. Majorana, E. & Nuovo, I. L. Teoria simmetrica dell’elettrone e del positrone. Cimento 14, 171–184 (1937).

    Article  MATH  Google Scholar 

  2. Nayak, C. et al. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Beenakker, C. Annihilation of colliding Bogoliubov quasiparticles reveals their Majorana nature. Phys. Rev. Lett. 112, 070604 (2014).

    Article  ADS  Google Scholar 

  4. 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).

    Article  ADS  Google Scholar 

  5. Das Sarma, S., Freedman, M. & Nayak, C. Topologically protected qubits from a possible non-Abelian fractional quantum Hall state. Phys. Rev. Lett. 94, 166802 (2005).

    Article  ADS  Google Scholar 

  6. 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).

    Article  ADS  Google Scholar 

  7. Tewari, S. et al. Quantum computation using vortices and Majorana zero modes of a px + ipy superfluid of fermionic cold atoms. Phys. Rev. Lett. 98, 010506 (2007).

    Article  ADS  Google Scholar 

  8. Fu, L. & Kane, C. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    Article  ADS  Google Scholar 

  9. Zhang, C. et al. px + ipy superfluid from s-wave interactions of fermionic cold atoms. Phys. Rev. Lett. 101, 160401 (2008).

    Article  ADS  Google Scholar 

  10. Sato, M., Takahashi, Y. & Fujimoto, S. Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms. Phys. Rev. Lett. 103, 020401 (2009).

    Article  ADS  Google Scholar 

  11. Sato, M. & Fujimoto, S. Topological phases of noncentrosymmetric superconductors: edge states, Majorana fermions and non-Abelian statistics. Phys. Rev. B 79, 094504 (2009).

    Article  ADS  Google Scholar 

  12. Sau, J. et al. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010).

    Article  ADS  Google Scholar 

  13. Lutchyn, R., Sau, J. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Sau, J. et al. Non-Abelian quantum order in spin–orbit-coupled semiconductors: search for topological Majorana particles in solid-state systems. Phys. Rev. B 82, 214509 (2010).

    Article  ADS  Google Scholar 

  16. Alicea, J. Majorana fermions in a tunable semiconductor device. Phys. Rev. B 81, 125318 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Bravyi, S. & Kitaev, A. Fermionic quantum computation. Ann. Phys. 298, 210–226 (2002).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Sengupta, K. et al. Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors. Phys. Rev. B 63, 144531 (2001).

    Article  ADS  Google Scholar 

  21. Flensberg, K. Tunneling characteristics of a chain of Majorana bound states. Phys. Rev. B 82, 180516 (2010).

    Article  ADS  Google Scholar 

  22. Law, K. T., Lee, P. A. & Ng, T. K. Majorana fermion induced resonant Andreev reflection. Phys. Rev. Lett. 103, 237001 (2009).

    Article  ADS  Google Scholar 

  23. Wimmer, M. et al. Quantum point contact as a probe of a topological superconductor. New J. Phys. 13, 053016 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. 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).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Finck, A. et al. Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device. Phys. Rev. Lett. 110, 126406 (2013).

    Article  ADS  Google Scholar 

  29. Kwon, H., Sengupta, K. & Yakovenko, V. Fractional a.c. Josephson effect in p- and d-wave superconductors. Eur. Phys. J. B 37, 349–361 (2004).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  31. Chang, W. et al. Hard gap in epitaxial semiconductor–superconductor nanowires. Nat. Nanotechnol. 10, 232–236 (2015).

    Article  ADS  Google Scholar 

  32. Takei, S. et al. Soft superconducting gap in semiconductor Majorana nanowires. Phys. Rev. Lett. 110, 186803 (2013).

    Article  ADS  Google Scholar 

  33. Sau, J., Tewari, S. & Das Sarma, S. Experimental and materials considerations for the topological superconducting state in electron- and hole-doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures. Phys. Rev. B 85, 064512 (2012).

    Article  ADS  Google Scholar 

  34. Sau, J. & Das Sarma, S. Density of states of disordered topological superconductor-semiconductor hybrid nanowires. Phys. Rev. B 88, 064506 (2013).

    Article  ADS  Google Scholar 

  35. Liu, C. et al. Andreev bound states versus Majorana bound states in quantum dot-nanowire-superconductor hybrid structures: trivial versus topological zero-bias conductance peaks. Phys. Rev. B 96, 075161 (2017).

    Article  ADS  Google Scholar 

  36. Chiu, C., Sau, J. & Das Sarma, S. Conductance of a superconducting Coulomb-blockaded Majorana nanowire. Phys. Rev. B 96, 054504 (2017).

    Article  ADS  Google Scholar 

  37. Pan, H. & Das Sarma, S. Physical mechanisms for zero-bias conductance peaks in Majorana nanowires. Phys. Rev. Res. 2, 013377 (2020).

    Article  Google Scholar 

  38. Das Sarma, S. & Pan, H. Disorder-induced zero-bias peaks in Majorana nanowires. Phys. Rev. B 103, 195158 (2021).

    Article  ADS  Google Scholar 

  39. Pan, H. et al. Generic quantized zero-bias conductance peaks in superconductor-semiconductor hybrid structures. Phys. Rev. B 101, 024506 (2020).

    Article  ADS  Google Scholar 

  40. Kells, G., Meidan, D. & Brouwer, P. Near-zero-energy end states in topologically trivial spin-orbit coupled superconducting nanowires with a smooth confinement. Phys. Rev. B 86, 100503 (2012).

    Article  ADS  Google Scholar 

  41. Akhmerov, A. et al. Quantized conductance at the Majorana phase transition in a disordered superconducting wire. Phys. Rev. Lett. 106, 057001 (2011).

    Article  ADS  Google Scholar 

  42. Liu, J. et al. Zero-bias peaks in the tunneling conductance of spin-orbit-coupled superconducting wires with and without Majorana end-states. Phys. Rev. Lett. 109, 267002 (2012).

    Article  ADS  Google Scholar 

  43. Bagrets, D. & Altland, A. Class D spectral peak in Majorana quantum wires. Phys. Rev. Lett. 109, 227005 (2012).

    Article  ADS  Google Scholar 

  44. Albrecht, S. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).

    Article  ADS  Google Scholar 

  45. Deng, M. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).

    Article  ADS  Google Scholar 

  46. Frolov, S. Quantum computing’s reproducibility crisis: Majorana fermions. Nature 592, 350–352 (2021).

    Article  ADS  Google Scholar 

  47. Zhang, H. et al. Large zero-bias peaks in InSb-Al hybrid semiconductor-superconductor nanowire devices. Preprint at https://arxiv.org/abs/2101.11456 (2021).

  48. Nichele, F. et al. Scaling of Majorana zero-bias conductance peaks. Phys. Rev. Lett. 119, 136803 (2017).

    Article  ADS  Google Scholar 

  49. Ahn, S. et al. Estimating disorder and its adverse effects in semiconductor Majorana nanowires. Phys. Rev. Mater. 5, 124602 (2021).

    Article  Google Scholar 

  50. Woods, B. D., Sarma, S. D. & Stanescu, T. D. Charge-impurity effects in hybrid Majorana nanowires. Phys. Rev. Appl. 16, 054053 (2021).

    Article  ADS  Google Scholar 

  51. Aghaee, M. et al. InAs-Al hybrid devices passing the topological gap protocol. Preprint at https://arxiv.org/abs/2207.02472 (2022).

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Correspondence to Sankar Das Sarma.

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Das Sarma, S. In search of Majorana. Nat. Phys. 19, 165–170 (2023). https://doi.org/10.1038/s41567-022-01900-9

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