Abstract
The discovery of topological insulators (TIs) has pointed out a new route to construct two dimensional electronic systems. These two dimensional electronic systems reside on surfaces of 3D TIs and are known to be robust against non-magnetic perturbations. Experimentally, however, it is known that surfaces of grown 3D TIs are not flat and are composed of rough terraces. Here we investigate effects of surface roughness on transport properties of three dimensional topological insulators. It is shown that surface roughness induces spin connection correction to Dirac fermions. By considering surface roughness in the roughnening phase, we construct effective Hamiltonian due to vortices configuration of roughness. Through the effective Hamiltonian, we find the scattering cross section and the corresponding conductivity. Our analyses indicate that even in the rough phase, the conductivity of Dirac fermions still resemble that of flat surfaces. The roughness induces mild change on transport properties of Dirac fermions on surfaces of 3D TIs.