Abstract: 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.
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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.
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(3):1652-1686.
Parente, Vincenzo; Campagnano, Gabriele; Giuliano, Domenico; Tagliacozzo, Arturo; Guinea, Francisco. 2014. "Topological Defects in Topological Insulators and Bound States at Topological Superconductor Vortices." Materials 7, no. 3: 1652-1686.