Electrons on the surface of topological insulators

Topological insulators are featured with massless surface states that are protected from impurity scattering. Electrons in such states move on the surface, which are usually curved. How would this curvature affect the motions ? This article [Phys. Rev. B 82, 085312 (Published August 12, 2010)] shows that, the electrons shall feel gravity-like force.

Electron scattering in solids is normally associated with impurities, defects, lattice vibrations, and electron-electron Coulomb scattering. Now, in an article published in Physical Review B, Jan Dahlhaus and collaborators from the Instituut-Lorentz at the University of Leiden in the Netherlands show that for surface electrons on a topological insulator, electron scattering can be dominated by a completely different mechanism: geodesic scattering. Geodesics are the generalization of straight lines in curved space. In general relativity, gravitational fields curve four-dimensional spacetime, and particle motion follows geodesic lines shaped by gravity. Strong enough fields cause the phenomenon known as gravitational lensing, an observable deflection of massless particles such as photons.

The surface electrons of a topological insulator behave as massless particles and are constrained to move in a two-dimensional curved space. The curvature is caused by random surface deformations that appear naturally during the growth of the material. Such a bump on the surface acts like a gravitational lens for surface electrons, resulting in trajectories that are analogous to geodesic motion. Considering that due to the special nature of topological insulators these surface electrons are protected from the ubiquitous impurity backscattering, this article likely reveals a previously unsuspected and important contribution to the resistivity on the surface of these materials. – Athanasios Chantis