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Materials 2014, 7(3), 1652-1686; doi:10.3390/ma7031652

Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices

1,2,*  and 5
1 Dipartimento di Fisica, Università di Napoli Federico II, Via Cintia, Napoli 80126, Italy 2 Consiglio Nazionale delle Ricerche - Superconductors, Oxides and other Innovative Materials and Devices (CNR-SPIN), Via Cintia, Napoli 80126, Italy 3 Dipartimento di Fisica, Università della Calabria Arcavacata di Rende, Cosenza I-87036, Italy 4 Istituto Nazionale Fisica Nucleare, Gruppo Collegato di Cosenza, Arcavacata di Rende, Cosenza I-87036, Italy 5 Instituto de Ciencia de Materiales de Madrid, Consejo Superior Investigación Cientifica (ICMM-CSIC), Cantoblanco, Cale Sor Juana Ines de la Cruz 3, Madrid 28049, Spain
* Author to whom correspondence should be addressed.
Received: 9 September 2013 / Revised: 10 February 2014 / Accepted: 11 February 2014 / Published: 4 March 2014
(This article belongs to the Special Issue Spintronics)
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The scattering of Dirac electrons by topological defects could be one of the most relevant sources of resistance in graphene and at the boundary surfaces of a three-dimensional topological insulator (3D TI). In the long wavelength, continuous limit of the Dirac equation, the topological defect can be described as a distortion of the metric in curved space, which can be accounted for by a rotation of the Gamma matrices and by a spin connection inherited with the curvature. These features modify the scattering properties of the carriers. We discuss the self-energy of defect formation with this approach and the electron cross-section for intra-valley scattering at an edge dislocation in graphene, including corrections coming from the local stress. The cross-section contribution to the resistivity, ρ, is derived within the Boltzmann theory of transport. On the same lines, we discuss the scattering of a screw dislocation in a two-band 3D TI, like Bi1-xSbx, and we present the analytical simplified form of the wavefunction for gapless helical states bound at the defect. When a 3D TI is sandwiched between two even-parity superconductors, Dirac boundary states acquire superconductive correlations by proximity. In the presence of a magnetic vortex piercing the heterostructure, two Majorana states are localized at the two interfaces and bound to the vortex core. They have a half integer total angular momentum each, to match with the unitary orbital angular momentum of the vortex charge.
Keywords: Dirac electrons; topological defects; two-band topological insulators; Majorana bound state Dirac electrons; topological defects; two-band topological insulators; Majorana bound state
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Parente, V.; Campagnano, G.; Giuliano, D.; Tagliacozzo, A.; Guinea, F. Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices. Materials 2014, 7, 1652-1686.

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