nLab Majorana zero mode

Idea

In solid state physics, the term “Majorana zero mode” (often abbreviated “MZM” or just “Majorana”) has come to refer to (hypothetical and so far elusive) ground states of certain effectively 1-dimensional quantum materials (quantum/nano-wires) which are acted on by a “Majorana operator” (namely the Hermitian combination $c + c^\dagger$ of fermion annihilation/creation operators, only vaguely related to relativistic Majorana spinors) and which have been argued to potentially behave like Majorana anyons, in some sense (beware that these modes, being stuck to wires, would not be mobile and hence would not admit adiabatic braiding operations in the usual sense, see here).

These Majorana zero modes were theoretically introduced in a spin chain model by Kitaev 2001 (“Kitaev spin chain”), originally as a theoretical toy example for gapped and degenerate ground states vaguely as expected for topological order, but then argued to be realizable on interfaces of superconductors with certain topological insulators by Fu & Kane 2008; and their experimental realization in super-/semi-conducting nano-wires has been proposed in Lutchyn, Say & Das Sarma 2010, Oreg, Refael, von Oppen 2010.

Following these proposals and especially after Microsoft Quantum (with QuTech at TU Delft) declared (Nov 2016) the concrete aim of realizing topological quantum computation based on topological qbits given by such “Majorana zero modes” (following the plan laid out in Das Sarma, Freedman & Nayak 15), the topic attracted enormous attention in solid state physics.

But prominent claims of experimental detection of (these kinds of) Majorana zero modes had to be retracted:

• by Nature in 2021

  [doi:10.1038/s41586-021-03373-x, doi:10.5281/zenodo.4587841, doi:10.5281/zenodo.4545812, TU Delft press release]

• by Nature in 2022 [doi:10.1038/s41586-022-04704-2]

• by Science in 2022 [doi:10.1126/science.adf7575], cf. further commentary by S.M. Frolov here;

• and a range of further claims are under similar criticism, see Frolov & Mourik 2020, Das Sarma & Pan 2021, Frolov, Mourik & Zuo 2022 and the extensive list here.

While some (probably most) researchers now dismiss the whole approach of “Majorana zero modes” (e.g. BSSA21, p. 3) there is a new claim of detection by Nayak 22 & MicrosoftQuantum 23 – but see cautionary commentary by Frolov & Mourik 22a, 22b, Frolov 22 and Das Sarma 22, p. 9.

References

General

The general strategy of realizing Majorana zero modes in supercondocuting/semiconducting nanowires is due to

• Alexei Kitaev, Unpaired Majorana fermions in quantum wires, Physics-Uspekhi, 44 10S (2001) 131-136 [arXiv:cond-mat/0010440, doi:10.1070/1063-7869/44/10S/S29]

• Liang Fu, Charles Kane, Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator, Phys. Rev. Lett. 100 (2008) 096407 [doi:10.1103/PhysRevLett.100.096407]

• Roman M. Lutchyn, Jay D. Sau, Sankar Das Sarma, Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures, Phys. Rev. Lett. 105 (2010) 077001 [doi:10.1103/PhysRevLett.105.077001]

• Yuval Oreg, Gil Refael, and Felix von Oppen, Helical Liquids and Majorana Bound States in Quantum Wires, Phys. Rev. Lett. 105 (2010) 177002 [doi:10.1103/PhysRevLett.105.177002]

• Lukasz Fidkowski, Alexei Kitaev, The effects of interactions on the topological classification of free fermion systems, Phys. Rev. B 81 (2010) 134509 [arXiv:0904.2197, doi:10.1103/PhysRevB.81.134509]

  (interacting generalization)

reviewed in:

• Pasquale Marra, Majorana nanowires for topological quantum computation: A tutorial, J. of Applied Physics 132 (2022) 231101 [arXiv:2206.14828, doi:10.1063/5.0102999]

Discussion in the context of topological quantum computation:

• Sankar Das Sarma, Michael Freedman, Chetan Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf 1 15001 (2015) $[$doi:10.1038/npjqi.2015.1$]$

General review and experimental status:

• Sergey M. Frolov, How do we discover MAJORANA PARTICLES in NANOWIRES?, talk via Instituto de Física, Universidade de São Paulo (May 2021) [video]

  41:25: No, we have not discovered Majorana particles in nanowires. Yes, we should be able to do it.

• Sankar Das Sarma, In search of Majorana, Nature Physics 19 (2023) 165-170 [arXiv:2210.17365, doi:10.1038/s41567-022-01900-9]

See also:

• Wikipedia, Majorana bound states

Non-Detection

On the general problem of distinguishing the expected effect from noise:

• Sankar Das Sarma, Haining Pan, Disorder-induced zero-bias peaks in Majorana nanowires, Phys. Rev. B 103 195158 (2021) [arXiv:2103.05628, doi:10.1103/PhysRevB.103.195158]

we believe that similar confirmation bias applies to many other topological discovery claims in the literature during 2000–2020 where a precise knowledge of what one is looking for has been the key factor in the discovery claim, with the experimental quantization results themselves not being sufficiently compelling. […] Our results certainly apply to most of the Majorana experiments during 2012–2021 in the literature.

• Koen Bertels, Tamara Sarac, Aritra Sarkar, Imran Ashraf, Quantum Computing – from NISQ to PISQ, IEEE Micro 41 (2021) 24-32 [arXiv:2106.11840v4, doi:10.1109/MM.2021.3099195]

p. 3: The quantum physics community is sufficiently aware that when certain qubit technologies do not produce any reasonable result after several years of effort, they should be gently removed from the list of quantum candidates. After working with the physics colleagues in Delft, we saw that happening with the Majorana qubits that could not be confirmed in any follow-up experiment.

• Sergey M. Frolov, Vincent Mourik, We cannot believe we overlooked these Majorana discoveries [arXiv:2203.17060, doi:10.5281/zenodo.6364928, conclusion on: p. 7]

Non-retracted claims of experimental realization of something in the direction of Majorana zero modes:

• Gerbold C. Ménard, Andrej Mesaros, Christophe Brun, François Debontridder, Dimitri Roditchev, Pascal Simon, Tristan Cren, Isolated pairs of Majorana zero modes in a disordered superconducting lead monolayer, Nat Commun 10 2587 (2019) $[$doi:10.1038/s41467-019-10397-5$]$

• Chetan Nayak, Microsoft has demonstrated the underlying physics required to create a new kind of qubit, Microsoft Research Blog (March 2022)

• M. Aghaee et al. (Microsoft Quantum), InAs-Al Hybrid Devices Passing the Topological Gap Protocol, Phys. Rev. B 107 245423 (2023) [doi:10.1103/PhysRevB.107.245423, arXiv:2207.02472, video presentation]

  
  

  with an accompanying caveat editorial:

  Randall D. Kamien, Jessica Thomas, Stephen E. Nagler, Anthony M. Begley, and Sarma Kancharla, Editorial: Transparency in Physical Review Articles, Phys. Rev. B 107 210001 (2023) [doi:10.1103/PhysRevB.107.210001]

  saying:

  “In this issue of Physical Review B, Aghaee et al. [1] report on an advancement towards the goal of topological quantum computing. While Physical Review readers are well aware that the many minutiæ of procedures, computations, and synthesis may be omitted in any particular dispatch, in this publication the intellectual property of the authors’ employer has prevented the release of some parameters of the studied devices that may be needed in order to reproduce them. As a reflection of the traditional values of the scholarly community, this is not in accordance with the usual norms of the Physical Review journals.”

but see commentary in:

• Sergey Frolov, Twitter:1671558089382957056 (21 June 2023)

• Karmela Padavic-Callaghan, Microsoft says its weird new particle could improve quantum computers — Researchers at Microsoft say they have created elusive quasiparticles called Majorana zero modes – but scientists outside the company are sceptical, New Scientist (21 June 2023) [web]

and earlier:

• Sergey M. Frolov, Vincent Mourik: Majorana Fireside Podcast, Episode 1: The Microsoft TGP paper live review [video, conclusion at: 1:01:31]

  1:01:52 The signal is fully consistent, from what we see, with not having discovered any Majorana or topological superconductivity here. At the same time, the amount of data is extremely narrow.

• Sergey M. Frolov, Superconductors and semiconductors, nanowires and majorana, research and integrity [video, general caution: 55:34, concrete criticism: 1:01:41]

  1:01:50: The claims of the discovery of Majorana have been overblown and are false. Majorana has not been discovered in nanowires. I don’t believe in any other system it has been discovered either.

On how this could happen:

• Elizabeth Gibney, Inside Microsoft’s quest for a topological quantum computer (Interview with Alex Bocharov), Nature (2016) [doi:10.1038/nature.2016.20774]

  [Bocharov:] We’re people-centric, rather than problem-centric.

See also:

• Sergey M. Frolov, So, You Think You Discovered a New State of Matter?, Physics 14 68 (2021) [physics.aps:v14/68]

• Sergey M. Frolov, Quantum computing’s reproducibility crisis: Majorana fermions, Nature 592 (2021) 350-352 [doi:10.1038/d41586-021-00954-8]

Anyons in topological superconductors

On anyon-excitations in topological superconductors.

via Majorana zero modes:

Original proposal:

• Nicholas Read, Dmitry Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect, Phys. Rev. B61:10267, 2000 (arXiv:cond-mat/9906453)

Review:

• Sankar Das Sarma, Michael Freedman, Chetan Nayak, Majorana Zero Modes and Topological Quantum Computation, npj Quantum Information 1, 15001 (2015) (nature:npjqi20151)

• Nur R. Ayukaryana, Mohammad H. Fauzi, Eddwi H. Hasdeo, The quest and hope of Majorana zero modes in topological superconductor for fault-tolerant quantum computing: an introductory overview (arXiv:2009.07764)

• Yusuke Masaki, Takeshi Mizushima, Muneto Nitta, Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors [arXiv:2301.11614]

Further developments:

• Meng Cheng, Victor Galitski, Sankar Das Sarma, Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors, Phys. Rev. B 84, 104529 (2011) (arXiv:1106.2549)

• Javad Shabani et al., Two-dimensional epitaxial superconductor-semiconductor heterostructures: A platform for topological superconducting networks, Phys. Rev. B 93 155402 (2016) [doi:10.1103/PhysRevB.93.155402, arXiv:1511.01127]

• Javad Shabani et al., Zero-Energy Modes from Coalescing Andreev States in a Two-Dimensional Semiconductor-Superconductor Hybrid Platform, Phys. Rev. Lett. 119 (2017) 176805 [doi:10.1103/PhysRevLett.119.176805, arXiv:1703.03699]

• Javad Shabani et al., Fusion of Majorana Bound States with Mini-Gate Control in Two-Dimensional Systems, Nature Communications 13 (2022) 1738-1747 [doi:10.1038/s41467-022-29463-6, arXiv:2101.09272]

• Javad Shabani et al., Quasiparticle dynamics in epitaxial Al-InAs planar Josephson junctions, PRX Quantum 4 030339 (2023) [doi:10.1103/PRXQuantum.4.030339, arXiv:2303.04784]

via Majorana zero modes restricted to edges of topological insulators:

• Biao Lian, Xiao-Qi Sun, Abolhassan Vaezi, Xiao-Liang Qi, and Shou-Cheng Zhang, Topological quantum computation based on chiral Majorana fermions, PNAS October 23, 2018 115 (43) 10938-10942; first published October 8, 2018 (doi:10.1073/pnas.1810003115)

See also:

• Yusuke Masaki, Takeshi Mizushima, Muneto Nitta, Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors $[$arXiv:2301.11614$]$