Drag effect and Cooper electron-hole pair fluctuations in a topological insulator film

Manifestations of fluctuating Cooper pairs formed by electrons and holes populating opposite surfaces of a topological insulator film in the Coulomb drag effect are considered. Fluctuational Aslamazov-Larkin contribution to the transresistance between surfaces of the film is calculated. The contribution is the most singular one in the vicinity of critical temperature $T_\mathrm{d}$ and diverges in the critical manner as $(T-T_\mathrm{d})^{-1}$. In the realistic conditions $\gamma\sim T_\mathrm{d}$, where $\gamma$ is average scattering rate of electrons and holes, Aslamazov-Larkin contribution plays important role and can dominate the fluctuation transport. The macroscopic theory based on time-dependent Ginzburg-Landau equation is developed for description of the fluctuational drag effect in the system. The results can be easily generalized for other realizations of electron-hole bilayer.