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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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## References

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

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

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

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).

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).

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).

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).

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

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

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).

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

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

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).

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

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).

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

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

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

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

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

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

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

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

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

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

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).

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).

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

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).

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).

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

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

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).

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

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).

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

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

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

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

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).

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

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).

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

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

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

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

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).

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

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

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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