Coulomb drag in topological insulator films

We study Coulomb drag between the top and bottom surfaces of topological insulator films. We derive a kinetic equation for the thin-film spin density matrix containing the full spin structure of the two-layer system, and analyze the electron-electron interaction in detail in order to recover all terms responsible for Coulomb drag. Focusing on typical topological insulator systems, with film thicknesses d up to 6 nm, we obtain numerical and approximate analytical results for the drag resistivity $\rho_\text{D}$ and find that $\rho_\text{D}$ is proportional to $T^2d^{-4}n^{-3/2}_{\text{a}}n^{-3/2}_{\text{p}}$ at low temperature T and low electron density $n_{\text{a,p}}$, with a denoting the active layer and p the passive layer. In addition, we compare $\rho_{\text{D}}$ with graphene, identifying qualitative and quantitative differences, and we discuss the multi valley case, ultra thin films and electron-hole layers.