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

• Published in: Materials 2014-03, Vol.7 (3), p.1652-1686
• Main Authors: Parente, Vincenzo, Campagnano, Gabriele, Giuliano, Domenico, Tagliacozzo, Arturo, Guinea, Francisco
• Format: Article
• Language: English
• Subjects: Defects; Electrons; Energy; Fluid flow; Graphene; Investigations; Nanowires; Scattering; Superconductors; Three dimensional; Topology; Vortices
• ISSN: 1996-1944; 1996-1944
• DOI: 10.3390/ma7031652

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 Bi Sb , 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.