Coulomb Drag in Normal Metals and Superconductors: Diagrammatic Approach

The diagrammatic linear response formalism for the Coulomb drag in two--layer systems is developed. This technique can be used to treat both elastic disorder and intralayer interaction effects. In the absence of intralayer electron--electron correlations we reproduce earlier results, obtained using the kinetic equation and the memory--function formalism. In addition we calculate weak--localization corrections to the drag coefficient and the Hall drag coefficient in a perpendicular magnetic field. As an example of the intralayer interaction effects we consider a situation where one (or both) layers are close to (but above) the superconducting transition temperature. Fluctuation corrections, analogous to the Aslamazov--Larkin corrections, to the drag coefficient are calculated. Although the fluctuation corrections do not enhance the drag coefficient for normal--superconductor systems, a dramatic enhancement is found for superconductor--superconductor structures.