LINEAR-RESPONSE THEORY OF COULOMB DRAG IN COUPLED ELECTRON-SYSTEMS

We report a fully microscopic theory for the transconductivity, or, equivalently, the momentum transfer rate, of Coulomb coupled electron systems. We use the Kubo linear-response formalism and our main formal result expresses the transconductivity in terms of two fluctuation diagrams, which are topologically related but not equivalent to the Aslamazov-Larkin diagrams known from superconductivity. Results reported elsewhere are shown to be special cases of our general expression; specifically, we recover the Boltzmann equation result in the semiclassical clean limit and the memory function results for dirty systems with constant impurity scattering rates. Furthermore, we show that for energy-dependent relaxation times, the final result is not expressible in terms of standard density-response functions. Other results include (i) at T = 0, the frequency dependence of the transfer rate is found to be proportional to Omega and Omega(2) for frequencies below and above the impurity scattering rate, respectively, and (ii) the weak localization correction to the transconductivity is given by delta sigma(21)(WL)proportional to delta sigma(11)(WL) +delta sigma(22)(WL).