Manipulating Majorana zero modes on atomic rings with an external magnetic field

Non-Abelian quasiparticles have been predicted to exist in a variety of condensed matter systems. Their defining property is that an adiabatic braid between two of them results in a non-trivial change of the quantum state of the system. The simplest non-Abelian quasiparticles—the Majorana bound states—can occur in one-dimensional electronic nano-structures proximity-coupled to a bulk superconductor. Here we propose a set-up, based on chains of magnetic adatoms on the surface of a thin-film superconductor, in which the control over an externally applied magnetic field suffices to create and manipulate Majorana bound states. We consider specifically rings of adatoms and show that they allow for the creation, annihilation, adiabatic motion and braiding of pairs of Majorana bound states by varying the magnitude and orientation of the external magnetic field.

[1]  C. Chamon,et al.  Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials , 2009, 0910.5921.

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

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

[4]  Jian Li,et al.  Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor , 2014, Science.

[5]  C. M. Marcus,et al.  Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover , 2013, 1303.2407.

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

[7]  P. Hyldgaard,et al.  Quantum confinement in monatomic Cu chains on Cu(111). , 2004, Physical review letters.

[8]  S. Tewari,et al.  Majorana fermions in semiconductor nanowires: fundamentals, modeling, and experiment , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[9]  Y. Luh.  BOUND STATE IN SUPERCONDUCTORS WITH PARAMAGNETIC IMPURITIES , 1965 .

[10]  M F Crommie,et al.  Confinement of Electrons to Quantum Corrals on a Metal Surface , 1993, Science.

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

[12]  Ali Yazdani,et al.  Probing the Local Effects of Magnetic Impurities on Superconductivity , 1997, Science.

[13]  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.

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

[15]  L. Glazman,et al.  Unconventional topological phase transitions in helical Shiba chains , 2013, 1312.5723.

[16]  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.

[17]  T. Ojanen,et al.  Majorana states in helical Shiba chains and ladders , 2013, 1308.6108.

[18]  N. Nilius,et al.  Development of One-Dimensional Band Structure in Artificial Gold Chains , 2002, Science.

[19]  D. Loss,et al.  Majorana qubit decoherence by quasiparticle poisoning , 2012, 1204.3326.

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

[21]  B. Bernevig,et al.  Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor , 2013, 1303.6363.

[22]  B. Braunecker,et al.  Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase. , 2013, Physical review letters.

[23]  D. Loss,et al.  Nuclear magnetism and electron order in interacting one-dimensional conductors , 2009, 0908.0904.

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

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

[26]  Y. Oreg,et al.  Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions , 2012, Nature Physics.

[27]  M. M. Vazifeh,et al.  Self-organized topological state with Majorana fermions. , 2013, Physical review letters.

[28]  D. Loss,et al.  Helical nuclear spin order in two-subband quantum wires , 2013, 1303.1542.

[29]  S. Sarma,et al.  Helical order in one-dimensional magnetic atom chains and possible emergence of Majorana bound states , 2014, 1401.7048.

[30]  P. Recher,et al.  Unpaired Majorana fermions in quantum wires , 2001 .

[31]  Hiroyuki Shiba,et al.  Classical Spins in Superconductors , 1968 .

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

[33]  Jian-Xin Zhu,et al.  Impurity-induced states in conventional and unconventional superconductors , 2004, cond-mat/0411318.

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

[35]  Jacek K. Furdyna,et al.  The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles , 2012, Nature Physics.

[36]  S. Heinze,et al.  Information transfer by vector spin chirality in finite magnetic chains. , 2012, Physical review letters.

[37]  L. Glazman,et al.  Topological superconducting phase in helical Shiba chains , 2013, 1308.3969.

[38]  Yukio Tanaka,et al.  Two-dimensional p -wave superconducting states with magnetic moments on a conventional s -wave superconductor , 2013, 1306.3686.

[39]  L. Fu,et al.  Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator , 2009 .

[40]  Guang-Yao Huang,et al.  Anomalous zero-bias conductance peak in a Nb-InSb nanowire-Nb hybrid device. , 2012, Nano letters.

[41]  W. Duan,et al.  High-resolution scanning tunneling spectroscopy of magnetic impurity induced bound states in the superconducting gap of Pb thin films. , 2008, Physical review letters.

[42]  C. L. Yu,et al.  Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device , 2012, 1204.4130.

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

[44]  D. Zumbühl,et al.  Possible evidence for helical nuclear spin order in GaAs quantum wires. , 2013, Physical review letters.

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

[46]  A. I. Rusinov.  On the Theory of Gapless Superconductivity in Alloys Containing Paramagnetic Impurities , 1969 .

[47]  D. Loss,et al.  Spin-selective Peierls transition in interacting one-dimensional conductors with spin-orbit interaction , 2010, 1004.0467.

[48]  K. T. Law,et al.  Majorana fermion induced nonlocal current correlations in spin-orbit coupled superconducting wires , 2012, 1212.5879.

[49]  Daniel Loss,et al.  Topological superconductivity and Majorana fermions in RKKY systems. , 2013, Physical review letters.

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

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

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