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Materials 2014, 7(3), 1652-1686;

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

Dipartimento di Fisica, Università di Napoli Federico II, Via Cintia, Napoli 80126, Italy
Consiglio Nazionale delle Ricerche - Superconductors, Oxides and other Innovative Materials and Devices (CNR-SPIN), Via Cintia, Napoli 80126, Italy
Dipartimento di Fisica, Università della Calabria Arcavacata di Rende, Cosenza I-87036, Italy
Istituto Nazionale Fisica Nucleare, Gruppo Collegato di Cosenza, Arcavacata di Rende, Cosenza I-87036, Italy
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)
Full-Text   |   PDF [712 KB, uploaded 4 March 2014]


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. View Full-Text
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 (CC BY 3.0).

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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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