Halperin, Bertrand I. and Oreg, Yuval and Stern, Ady and Refael, Gil and Alicea, Jason and von Oppen, Felix (2012) Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires. Physical Review B, 85 (14). Art. No. 144501. ISSN 1098-0121 http://resolver.caltech.edu/CaltechAUTHORS:20120502-145534850
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It has been proposed that localized zero-energy Majorana states can be realized in a two-dimensional network of quasi-one-dimensional semiconductor wires that are proximity coupled to a bulk superconductor. The wires should have strong spin-orbit coupling with appropriate symmetry, and their electrons should be partially polarized by a strong Zeeman field. Then, if the Fermi level is in an appropriate range, the wire can be in a topological superconducting phase, with Majorana states that occur at wire ends and at Y junctions, where three topological superconductor segments may be joined. Here we generalize these ideas to consider a three-dimensional network. The positions of Majorana states can be manipulated, and their non-Abelian properties made visible, by using external gates to selectively deplete portions of the network or by physically connecting and redividing wire segments. Majorana states can also be manipulated by reorientations of the Zeeman field on a wire segment, by physically rotating the wire about almost any axis, or by evolution of the phase of the order parameter in the proximity-coupled superconductor. We show how to keep track of sign changes in the zero-energy Hilbert space during adiabatic manipulations by monitoring the evolution of each Majorana state separately, rather than keeping track of the braiding of all possible pairs. This has conceptual advantages in the case of a three-dimensional network, and may be computationally useful even in two dimensions, if large numbers of Majorana sites are involved.
|Additional Information:||© 2012 American Physical Society. Received 28 December 2011; revised manuscript received 12 March 2012; published 2 April 2012. We thank Charles Marcus and Karsten Flensberg for helpful discussions. The work was funded by a Microsoft grant, NSF Grant No. DMR-0906475, NSF Grant No. DMR-0906475, BSF, Minerva, and SPP 1285 of the Deutsche Forschungsgemeinschaft. G.R. acknowledges funding provided by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation. We also acknowledge the hospitality of the Aspen Center for Physics and the Kavli Institute for Theoretical Physics (University of California, Santa Barbara).|
|Group:||Institute for Quantum Information and Matter, IQIM|
|Classification Code:||PACS: 03.67.Lx, 03.65.Vf, 03.67.Pp, 05.30.Pr|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||02 May 2012 22:59|
|Last Modified:||26 Dec 2012 15:09|
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