Electronic properties near extended defects in topological systems

Even though it is naively expected that topologically protected states are insensitive to disorder, in three-dimensional systems extended defects can significantly affect the local and transport properties usually assigned to topological states. We focus on line defects on topological insulator surfaces and planar defects in Weyl semimetals, which commonly occur in these systems. Conservation of particle current allows us to find boundary conditions for these sharply defined defects. We show that topological insulator surfaces with line defects in the presence of magnetic scattering and/or electrostatic potential host spin-textured 1D bound states. The dispersion and spin structure of these states can be controlled via an in-plane magnetic field. This leads to tunable spin accumulation near the defect and dissipation-less charge currents along the defect. We also calculate the spin-projected local density of states, which can be measured using a spin-resolved STM. Our framework is then extended to planar defects in Weyl semimetals, and we explore the conditions for stability of 2D bound states. We discuss pathways to control the properties of both 1D and 2D defect states, which will assist in building useful functionalities for devices based on these topological systems.