Search for Majorana Fermions in Superconductors

Majorana fermions (particles that are their own antiparticle) may or may not exist in nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference and a topological (Berry) phase to eliminate the energy difference from zero-point motion. A pair of widely separated Majorana fermions, bound to magnetic or electrostatic defects, has non-Abelian exchange statistics. A qubit encoded in this Majorana pair is expected to have an unusually long coherence time. I discuss strategies to detect Majorana fermions in a topological superconductor, as well as possible applications in a quantum computer. The status of the experimental search is reviewed.

[1]  Shinsei Ryu,et al.  Topological insulators and superconductors: tenfold way and dimensional hierarchy , 2009, 0912.2157.

[2]  G. Refael,et al.  Non-Abelian statistics and topological quantum information processing in 1D wire networks , 2010, 1006.4395.

[3]  S. Girvin,et al.  Charge-insensitive qubit design derived from the Cooper pair box , 2007, cond-mat/0703002.

[4]  G. Refael,et al.  Manipulating Majorana fermions using supercurrents , 2011, 1110.6193.

[5]  S. Das Sarma,et al.  Search for Majorana fermions in multiband semiconducting nanowires. , 2010, Physical review letters.

[6]  X. Qi,et al.  Conductance and noise signatures of Majorana backscattering , 2010, 1008.2003.

[7]  E. Bakkers,et al.  Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices , 2012, Science.

[8]  K. Flensberg,et al.  Majorana fermions in superconducting nanowires without spin-orbit coupling , 2011, 1111.2129.

[9]  L. Fu,et al.  Superconducting proximity effect and majorana fermions at the surface of a topological insulator. , 2007, Physical review letters.

[10]  M. Fisher,et al.  Quasiparticle localization in superconductors with spin-orbit scattering , 1999, cond-mat/9906290.

[11]  S Das Sarma,et al.  Generic new platform for topological quantum computation using semiconductor heterostructures. , 2009, Physical review letters.

[12]  K. Flensberg.  Tunneling characteristics of a chain of Majorana bound states , 2010, 1009.3533.

[13]  S. Das Sarma,et al.  Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. , 2010, Physical review letters.

[14]  C. Kane,et al.  Topological Defects and Gapless Modes in Insulators and Superconductors , 2010, 1006.0690.

[15]  S. Tewari,et al.  Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions. , 2011, Physical review letters.

[16]  Jason Alicea,et al.  Majorana fermions in a tunable semiconductor device , 2009, 0912.2115.

[17]  G. Volovik.  Fermion zero modes on vortices in chiral superconductors , 1999, cond-mat/9909426.

[18]  C. W. J. Beenakker,et al.  Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin-orbit coupling , 2011 .

[19]  A. Mirlin,et al.  Anderson Transitions , 2007, 0707.4378.

[20]  Liang Fu,et al.  Electron teleportation via Majorana bound states in a mesoscopic superconductor. , 2009, Physical review letters.

[21]  A. Potter,et al.  Topological superconductivity and Majorana fermions in metallic surface states , 2012, 1201.2176.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  A. Cook,et al.  Majorana fermions in a topological-insulator nanowire proximity-coupled to an s -wave superconductor , 2011 .

[24]  Mahn‐Soo Choi,et al.  Interferometric and noise signatures of Majorana fermion edge states in transport experiments. , 2011, Physical review letters.

[25]  C. Beenakker,et al.  Splitting of a Cooper pair by a pair of Majorana bound states. , 2008, Physical review letters.

[26]  C. Chamon,et al.  Decay rates for topological memories encoded with Majorana fermions , 2011, 1107.0288.

[27]  S. Das Sarma,et al.  Universal quantum computation in a semiconductor quantum wire network , 2010, 1007.4204.

[28]  Fusion rules and vortices in p x + i p y superconductors , 2005, cond-mat/0505515.

[29]  Mikhail I. Katsnelson.  Graphene by Mikhail I. Katsnelson , 2012 .

[30]  Haijun Zhang,et al.  Half-metallic surface states and topological superconductivity in NaCoO 2 from first principles , 2011, 1103.1930.

[31]  C. W. J. Beenakker,et al.  Anyonic interferometry without anyons: how a flux qubit can read out a topological qubit , 2010, 1005.3423.

[32]  G. Refael,et al.  Helical liquids and Majorana bound states in quantum wires. , 2010, Physical review letters.

[33]  Matveev,et al.  Anomalous Proximity Effect in the Nb-BiSb-Nb Junctions. , 1996, Physical review letters.

[34]  S. Fujimoto,et al.  Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms. , 2009, Physical review letters.

[35]  Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures , 1996, cond-mat/9602137.

[36]  Ettore Majorana.  Teoria simmetrica dell’elettrone e del positrone , 1937 .

[37]  C. Beenakker,et al.  Majorana bound states without vortices in topological superconductors with electrostatic defects. , 2010, Physical review letters.

[38]  Ady Stern,et al.  Anyons and the quantum Hall effect - a pedagogical review , 2007, 0711.4697.

[39]  F. Wilczek.  Majorana returns , 2009 .

[40]  D. Goldhaber-Gordon,et al.  Unconventional Josephson effect in hybrid superconductor-topological insulator devices. , 2012, Physical review letters.

[41]  M. Kriener,et al.  Topological Superconductivity in CuxBi2Se3 , 2011, 1108.1101.

[42]  E. Grosfeld,et al.  Unpaired Majorana fermions in a layered topological superconductor , 2011, 1102.0360.

[43]  David A. Huse,et al.  Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples , 2001 .

[44]  Proposed detection of the topological phase in ring-shaped semiconductor-superconductor nanowires using Coulomb blockade transport. , 2011, Physical review letters.

[45]  S. Fujimoto,et al.  Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors , 2010, 1006.4487.

[46]  Yi Cui,et al.  Signatures of Majorana Fermions in Hybrid Superconductor-Topological Insulator Devices , 2012 .

[47]  Chapter 6 Topological quantum computation away from the ground state with Majorana fermions , 2011 .

[48]  M. Salomaa,et al.  Mutual friction in superfluid 3He: Effects of bound states in the vortex core. , 1991, Physical review. B, Condensed matter.

[49]  Jian Li,et al.  Gate-tuned normal and superconducting transport at the surface of a topological insulator , 2011, Nature communications.

[50]  Masatoshi Sato,et al.  Topological phases of noncentrosymmetric superconductors: Edge states, Majorana fermions, and non-Abelian statistics , 2008, 0811.3864.

[51]  M. Leijnse,et al.  Scheme to measure Majorana fermion lifetimes using a quantum dot , 2010, 1012.4650.

[52]  G. Volovik,et al.  The Universe in a Helium Droplet , 2003 .

[53]  E. Demler,et al.  Observing Majorana bound states in p-wave superconductors using noise measurements in tunneling experiments. , 2006, Physical review letters.

[54]  D. Ivanov.  Non-Abelian statistics of half-quantum vortices in p-wave superconductors. , 2000, Physical review letters.

[55]  X. Qi,et al.  Topological superconducting phase and Majorana fermions in half-metal/superconductor heterostructures , 2010, 1011.6422.

[56]  Chuanwei Zhang,et al.  Testable signatures of quantum nonlocality in a two-dimensional chiral p-wave superconductor. , 2008, Physical review letters.

[57]  Q. Xue,et al.  Interplay between topological insulators and superconductors , 2011, 1105.6174.

[58]  N. Cooper,et al.  Structure and consequences of vortex-core states in p-wave superfluids , 2010, 1006.0924.

[59]  William Shockley,et al.  On the Surface States Associated with a Periodic Potential , 1939 .

[60]  A. R. Akhmerov.  Topological quantum computation away from the ground state using Majorana fermions , 2010 .

[61]  A. Kitaev.  Unpaired Majorana fermions in quantum wires , 2000, cond-mat/0010440.

[62]  V. Yakovenko,et al.  Theoretical Prediction of the Fractional ac Josephson Effect in p- and d-Wave Superconductors , 2002 .

[63]  Junren Shi,et al.  Superconducting phase with a chiral f-wave pairing symmetry and Majorana fermions induced in a hole-doped semiconductor. , 2010, Physical review letters.

[64]  S. Tewari,et al.  Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires , 2010, 1012.0561.

[65]  K. T. Law,et al.  Robustness of Majorana fermion induced fractional Josephson effect in multichannel superconducting wires , 2011, 1103.5013.

[66]  C. Beenakker,et al.  Quantized conductance at the Majorana phase transition in a disordered superconducting wire. , 2010, Physical review letters.

[67]  T. Neupert,et al.  Chain of Majorana states from superconducting Dirac fermions at a magnetic domain wall. , 2010, Physical review letters.

[68]  R. Jackiw,et al.  Zero modes of the vortex-fermion system , 1981 .

[69]  R. Egger,et al.  Coulomb blockade of Majorana fermion induced transport , 2011 .

[70]  Stretched quantum states emerging from a Majorana medium , 2007 .

[71]  T. Yokoyama,et al.  Manipulation of the Majorana fermion, Andreev reflection, and Josephson current on topological insulators. , 2009, Physical review letters.

[72]  P. Lee.  Proposal for Creating a Spin-polarized p_x+ip_y State and Majorana Fermions , 2009, 0907.2681.

[73]  Yukio Tanaka,et al.  Tunneling between two helical superconductors via Majorana edge channels. , 2010, Physical review letters.

[74]  T. Yokoyama,et al.  Unconventional superconductivity on a topological insulator. , 2009, Physical Review Letters.

[75]  A. Stern,et al.  Majorana fermions on a disordered triangular lattice , 2011, 1106.6272.

[76]  Meng Cheng,et al.  Topological protection of Majorana qubits , 2011, 1112.3662.

[77]  Yize Jin,et al.  Topological insulators , 2014, Topology in Condensed Matter.

[78]  A. Mirlin,et al.  Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class-D thermal quantum Hall effect , 2006, cond-mat/0610700.

[79]  A. Potter,et al.  Multichannel generalization of Kitaev's Majorana end states and a practical route to realize them in thin films. , 2010, Physical review letters.

[80]  Xiao-Liang Qi,et al.  Chiral topological superconductor from the quantum Hall state , 2010, 1003.5448.

[81]  S. Papanikolaou,et al.  Straining topological insulators as a way to detect Majorana fermions , 2011 .

[82]  M. Gibertini,et al.  Josephson-Majorana cycle in topological single-electron hybrid transistors , 2012, 1202.6357.

[83]  Xiao Hu,et al.  Detecting Majorana fermions by nonlocal entanglement between quantum dots , 2013 .

[84]  C. Caroli,et al.  Bound Fermion states on a vortex line in a type II superconductor , 1964 .

[85]  G. Sullivan,et al.  Andreev reflection of helical edge modes in InAs/GaSb quantum spin Hall insulator. , 2011, Physical review letters.

[86]  Y. Nazarov,et al.  Topological properties of superconducting junctions , 2011, 1103.0780.

[87]  N. Read,et al.  Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect , 1999, cond-mat/9906453.

[88]  S. Fujimoto,et al.  Existence of Majorana fermions and topological order in nodal superconductors with spin-orbit interactions in external magnetic fields. , 2010, Physical review letters.

[89]  P. Brouwer,et al.  Andreev reflection from noncentrosymmetric superconductors and Majorana bound-state generation in half-metallic ferromagnets , 2010, 1011.5839.

[90]  C. Beenakker,et al.  Electrically detected interferometry of Majorana fermions in a topological insulator. , 2009, Physical review letters.

[91]  C. Kane,et al.  Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction , 2008, 0804.4469.

[92]  Jason Alicea,et al.  New directions in the pursuit of Majorana fermions in solid state systems , 2012, Reports on progress in physics. Physical Society.

[93]  M. Gingras.  Observing Monopoles in a Magnetic Analog of Ice , 2009, Science.

[94]  S. Sarma,et al.  Realizing a robust practical Majorana chain in a quantum-dot-superconductor linear array , 2011, Nature Communications.

[95]  Electric-field-induced Majorana fermions in armchair carbon nanotubes. , 2011, Physical review letters.

[96]  L. Fu,et al.  Probing neutral Majorana fermion edge modes with charge transport. , 2009, Physical review letters.

[97]  M. Katsnelson.  Graphene: Carbon in Two Dimensions , 2006, cond-mat/0612534.

[98]  Cenke Xu,et al.  Fractionalization in Josephson junction arrays hinged by quantum spin Hall edges , 2009, 0911.1782.

[99]  K. T. Law,et al.  Majorana fermion induced resonant Andreev reflection. , 2009, Physical review letters.

[100]  Unconventional Josephson signatures of Majorana bound states. , 2011, Physical review letters.

[101]  F. Hassler,et al.  Dynamical detection of Majorana fermions in current-biased nanowires , 2012, 1202.0642.

[102]  Disordered 2d quasiparticles in class D: Dirac fermions with random mass, and dirty superconductors , 1999, cond-mat/9910480.

[103]  P. Ioselevich,et al.  Anomalous Josephson current via Majorana bound states in topological insulators. , 2010, Physical Review Letters.

[104]  R. Žitko.  Detection of Majorana edge states in topological superconductors through non-Fermi-liquid effects induced in an interacting quantum dot , 2011, 1102.0973.

[105]  C. Beenakker,et al.  Coulomb stability of the 4π-periodic Josephson effect of Majorana fermions , 2011, 1108.1095.

[106]  Q. Xue,et al.  The Coexistence of Superconductivity and Topological Order in the Bi2Se3 Thin Films , 2011, Science.

[107]  R. Egger,et al.  Supercurrent blockade in Josephson junctions with a Majorana wire , 2012, 1202.0438.

[108]  S. Simon,et al.  Majorana fermions of a two-dimensional p x + i p y superconductor , 2009, 0904.2920.

[109]  Gregory W. Moore,et al.  Nonabelions in the fractional quantum Hall effect , 1991 .

[110]  R. Aguado,et al.  ac Josephson effect in finite-length nanowire junctions with Majorana modes. , 2011, Physical review letters.

[111]  A. Kitaev.  Fault tolerant quantum computation by anyons , 1997, quant-ph/9707021.

[112]  S. Sarma,et al.  Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortices in a p x + i p y superconductor , 2005, cond-mat/0510553.

[113]  Nonlocal Hanbury?Brown?Twiss interferometry and entanglement generation from Majorana bound states , 2011 .

[114]  H. Baranger,et al.  Detecting a Majorana-Fermion Zero Mode Using a Quantum Dot , 2011, 1107.4338.

[115]  Paul Adrien Maurice Dirac,et al.  A Theory of Electrons and Protons , 1930 .

[116]  J. C. Budich,et al.  Failure of protection of Majorana based qubits against decoherence , 2011, 1111.1734.

[117]  M. Veldhorst,et al.  Experimental realization of superconducting quantum interference devices with topological insulator junctions , 2012 .

[118]  Y. Nazarov,et al.  Phenomenology and dynamics of a Majorana Josephson junction , 2011, 1112.6368.

[119]  T. M. Klapwijk,et al.  Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion , 1982 .

[120]  A. Eddington.  A Symmetrical Treatment of the Wave Equation , 1928 .

[121]  C. Beenakker,et al.  Quantum point contact as a probe of a topological superconductor , 2011, 1101.5795.

[122]  X. Qi,et al.  Topological insulators and superconductors , 2010, 1008.2026.

[123]  Frank Wilczek,et al.  2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states , 1996 .

[124]  B. Trauzettel,et al.  Detecting Majorana bound states by nanomechanics , 2011, 1108.2607.

[125]  Si Wu,et al.  Non-Abelian topological superconductors from topological semimetals and related systems under the superconducting proximity effect , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[126]  Diamagnetism of graphite , 1973 .

[127]  S. Simon,et al.  Non-Abelian Anyons and Topological Quantum Computation , 2007, 0707.1889.

[128]  Michael Tinkham,et al.  Introduction to Superconductivity , 1975 .

[129]  D. Loss,et al.  Majorana edge states in interacting one-dimensional systems. , 2010, Physical review letters.

[130]  C. Beenakker,et al.  Coulomb-assisted braiding of Majorana fermions in a Josephson junction array , 2011, 1111.6001.

[131]  A. Vishwanath,et al.  Majorana modes at the ends of superconductor vortices in doped topological insulators. , 2010, Physical review letters.

[132]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[133]  C. Beenakker,et al.  The top-transmon: a hybrid superconducting qubit for parity-protected quantum computation , 2011, 1105.0315.

[134]  C. W. J. Beenakker,et al.  Effective mass and tricritical point for lattice fermions localized by a random mass , 2010, 1004.1111.

[135]  G. Refael,et al.  Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires , 2011, 1112.5333.

[136]  B. B'eri,et al.  Dephasing-enabled triplet Andreev conductance , 2009, 0903.2190.

[137]  Majorana modes in time-reversal invariant s-wave topological superconductors. , 2011, Physical review letters.

[138]  A. Stern,et al.  Observing Majorana bound states of Josephson vortices in topological superconductors , 2010, Proceedings of the National Academy of Sciences.

[139]  F. Nori,et al.  Majorana fermions in pinned vortices , 2011, 1106.6131.

[140]  A. Morpurgo,et al.  Majorana fermions in superconducting helical magnets , 2011, 1110.5637.

[141]  Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors , 2000, cond-mat/0010206.

[142]  J. Jain,et al.  Superconducting proximity effect and possible evidence for Pearl vortices in a candidate topological insulator , 2011, 1106.3605.