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| Majorana zero modes | |
|---|---|
| Name | Majorana zero modes |
| Field | Condensed matter physics |
| Discovered | 1937 |
| Discoverer | Ettore Majorana |
Majorana zero modes are emergent quasiparticles predicted to occur as zero-energy bound states in certain condensed matter systems, with non-Abelian exchange statistics that have potential applications in topological quantum computation. They connect concepts from Ettore Majorana, Enrico Fermi, Paul Dirac, Wolfgang Pauli, Richard Feynman, and John von Neumann to experimental platforms explored by groups at institutions such as Microsoft Research, IBM Research, Harvard University, Stanford University, and California Institute of Technology. The study of these modes links theoretical frameworks developed by Alexei Kitaev, Nikolai Bogoliubov, Lev Landau, Philip W. Anderson, and Anthony Leggett with materials discovered in work by Georges Bardeen, John Bardeen, Leon Cooper, Kitaev-related models, and experimental techniques advanced at facilities like CERN, Max Planck Society, Lawrence Berkeley National Laboratory, Bell Labs, and Los Alamos National Laboratory.
Majorana zero modes arise when quasiparticle excitations satisfy self-conjugation conditions proposed by Ettore Majorana and later contextualized by Paul Dirac and Enrico Fermi in relativistic quantum mechanics; condensed matter realizations adapt these ideas following formal developments by Alexei Kitaev and Nikolai Bogoliubov. Interest intensified after proposals from groups including Sankar Das Sarma, Roman Lutchyn, Jay D. Sau, K. T. Law, C. L. Kane, and Matthew P. A. Fisher predicted zero-energy states in hybrid structures combining superconductivity and low-dimensional electronic systems. Experimental efforts led by teams at Microsoft Research, Stanford University, Harvard University, University of California, Santa Barbara, Weizmann Institute of Science, and University of Copenhagen have sought signatures using techniques refined at Argonne National Laboratory, Oak Ridge National Laboratory, and Brookhaven National Laboratory.
The theoretical foundation builds on concepts from Bardeen–Cooper–Schrieffer (BCS) theory and the Bogoliubov–de Gennes formalism developed by Nikolai Bogoliubov and colleagues, incorporating ideas from topological band theory developed by Charles Kane, Eugene Mele, and Shoucheng Zhang. Key models include the Kitaev chain introduced by Alexei Kitaev, spinless p-wave superconductor models discussed by Anthony Leggett and Gregory Volovik, and heterostructure analyses by Roman Lutchyn and Sankar Das Sarma. Mathematical tools leverage methods from Clifford algebraes used by Élie Cartan and Hermann Weyl, representation theory inspired by Eugene Wigner, and topology concepts advanced by Henri Poincaré, Michael Atiyah, Isadore Singer, William Thurston, and John Milnor.
Proposed and pursued platforms include semiconductor-superconductor hybrids using materials such as InSb and InAs proximitized by superconductors like Al and Nb, ferromagnetic atomic chains on superconductors investigated by teams at Microsoft Research and Institute for Quantum Computing, vortex cores in iron-based superconductors discovered in studies at Chinese Academy of Sciences and Max Planck Institute for Chemical Physics of Solids, and engineered systems in topological insulators such as Bi2Se3 layered with Nb and Pb. Cold atom implementations and photonic analogues have been proposed by groups at MIT, ETH Zurich, University of Chicago, and University of Cambridge. Synthetic approaches draw on heterostructure fabrication techniques pioneered at IBM and Bell Labs and characterization via instruments at National Institute of Standards and Technology and European Synchrotron Radiation Facility.
Signatures sought experimentally include zero-bias conductance peaks measured in tunneling spectroscopy experiments performed by groups at Stanford University, Delft University of Technology, Harvard University, and University of Maryland; fractional Josephson effect observations pursued at University of California, Santa Barbara and Yale University; interferometry schemes proposed by Chetan Nayak and tested by collaborations involving Microsoft Research and Princeton University; and scanning tunneling microscopy (STM) imaging of localized zero-energy states in chains and vortices carried out by teams at IBM Research, Max Planck Institute, Lawrence Berkeley National Laboratory, and Weizmann Institute of Science. Noise spectroscopy, thermal conductance measurements, and Coulomb blockade phenomena have been reported in experiments at Argonne National Laboratory, Oak Ridge National Laboratory, Brookhaven National Laboratory, and Los Alamos National Laboratory.
Majorana-based approaches form the basis of proposals for topological quantum computation described by Alexei Kitaev, Michael Freedman, Chetan Nayak, Sankar Das Sarma, and Steven Simon; companies and consortia including Microsoft, Google Quantum AI, Rigetti Computing, Quantinuum, and IBM have explored implementations. Fault-tolerant qubits based on non-Abelian braiding aim to leverage work from Peter Shor and Andrew Steane on error correction, integrating with architectures proposed by Bruce Kane and Leo Kouwenhoven-inspired device concepts. Protocols for fusion-rule tests, measurement-only braiding, and Majorana teleportation have been advanced by Vadim Oganesyan, Jason Alicea, Roman Lutchyn, and Jay D. Sau.
Open issues include unambiguous discrimination of true non-Abelian zero modes from trivial low-energy states studied by Leo Kouwenhoven, Jörg Schmiedmayer, Charles Marcus, and Christopher M. Marcus; material disorder problems explored at Stanford University, Harvard University, and University of Basel; scalable fabrication challenges faced by Intel and Samsung-supported labs; and theoretical questions about interactions and many-body localization addressed by Matthew Fisher, Subir Sachdev, Patrick Lee, and Andrey Chubukov. Debates continue regarding reproducibility of zero-bias peaks reported by teams at Delft University of Technology, University of Copenhagen, University of Maryland, and Princeton University.
Mathematical descriptions employ Bogoliubov–de Gennes Hamiltonians rooted in work by Nikolai Bogoliubov, topological invariants like the Kitaev invariant inspired by Alexei Kitaev, and classification schemes related to the tenfold way developed by Andrei Altland and Martin R. Zirnbauer. Exact solutions and numerical studies draw on techniques from Bethe ansatz literature linked to Hans Bethe, tensor network methods advanced by Guifre Vidal and Frank Verstraete, and density functional theory implementations refined by Walter Kohn and Lu Jeu Sham. Computational studies use tools and platforms developed by Lawrence Livermore National Laboratory, Los Alamos National Laboratory, Sandia National Laboratories, National Center for Supercomputing Applications, and XSEDE.