Effect of surface curvature on conductivity in 3D topological insulator

The surface spectrum of a three-dimensional (3D) topological insulator consists of massless Dirac fermions. Hence, an electron moving on a curved surface in a 3D topological insulator follows a geodesic trajectory, akin to a photon in curved space. In this work, we study electron scattering due to the surface roughness (defects) modeled as a curved surface. The resulting effect on conductivity is estimated using the Boltzmann Equation. This scattering mechanism leads to a distinguishable signature of the conductivity on the electron density.