Probability Distribution of Majorana End-State Energies in Disordered Wires

被引:154
作者
Brouwer, Piet W. [1 ]
Duckheim, Mathias [1 ]
Romito, Alessandro [1 ]
von Oppen, Felix [1 ]
机构
[1] Free Univ Berlin, Dahlem Ctr Complex Quantum Syst & Fachbereich Phy, D-14195 Berlin, Germany
关键词
OFF-DIAGONAL DISORDER; QUANTUM COMPUTATION; ANYONS; CHAINS;
D O I
10.1103/PhysRevLett.107.196804
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy epsilon(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of epsilon(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level epsilon(1) has an algebraic tail at small epsilon(1). Our findings have implications for the speed at which a topological quantum computer can be operated.
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页数:4
相关论文
共 29 条
[1]   Non-Abelian statistics and topological quantum information processing in 1D wire networks [J].
Alicea, Jason ;
Oreg, Yuval ;
Refael, Gil ;
von Oppen, Felix ;
Fisher, Matthew P. A. .
NATURE PHYSICS, 2011, 7 (05) :412-417
[2]   Random-matrix theory of quantum transport [J].
Beenakker, CWJ .
REVIEWS OF MODERN PHYSICS, 1997, 69 (03) :731-808
[3]  
Brouwer P. W., PHYS REV B IN PRESS
[4]   Density of states in coupled chains with off-diagonal disorder [J].
Brouwer, PW ;
Mudry, C ;
Furusaki, A .
PHYSICAL REVIEW LETTERS, 2000, 84 (13) :2913-2916
[5]   Topological superconducting phase and Majorana fermions in half-metal/superconductor heterostructures [J].
Chung, Suk Bum ;
Zhang, Hai-Jun ;
Qi, Xiao-Liang ;
Zhang, Shou-Cheng .
PHYSICAL REVIEW B, 2011, 84 (06)
[6]   Andreev reflection from noncentrosymmetric superconductors and Majorana bound-state generation in half-metallic ferromagnets [J].
Duckheim, Mathias ;
Brouwer, Piet W. .
PHYSICAL REVIEW B, 2011, 83 (05)
[7]   SINGULAR BEHAVIOR OF TIGHT-BINDING CHAINS WITH OFF-DIAGONAL DISORDER [J].
EGGARTER, TP ;
RIEDINGER, R .
PHYSICAL REVIEW B, 1978, 18 (02) :569-575
[8]   Tunneling characteristics of a chain of Majorana bound states [J].
Flensberg, Karsten .
PHYSICAL REVIEW B, 2010, 82 (18)
[9]   Limit, logic, and computation [J].
Freedman, MH .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1998, 95 (01) :95-97
[10]   Superconducting proximity effect and Majorana fermions at the surface of a topological insulator [J].
Fu, Liang ;
Kane, C. L. .
PHYSICAL REVIEW LETTERS, 2008, 100 (09)