Coulomb drag in coupled 2D-2D and 2D-1D cylindrical quantum wells

To study the Coulomb drag resistivity of barrier-coupled 2D-1D and 2D-2D systems as well as the transition behaviour between them, we suggest investigation of a system which is composed of a couple of barrier-separated cylindrical S quantum wells (CDWs) with a common cylindrical symmetry axis. We find that for coupled 2D-1D CDWs, the momentum relaxation rate, tau _D^-1, is approximately proportional to T⁴, while for coupled 2D-2D CDWs, it is proportional to T² which is in accord with the characteristic behaviour of the momentum relaxation rate in coupled 2D-2D planes. In the transition region from coupled 2D-1D to 2D-2D CDWs, tau _D^-1 is proportional to Tⁿ with n reduced from 4 to 2 gradually. In addition, quite unlike the approximate d(^-2.4)-dependence of momentum relaxation rate divided by T_max² in coupled 2D-2D planes, due to the quantization of the circular motion round a cylindrical symmetry axis, for coupled 2D-1D CDWs the momentum relaxation rate divided by T_max⁴ is approximately proportional to d^-3 times a nearly periodic function of d, while for coupled 2D-2D CDWs, the momentum relaxation rate divide by T_max² is approximately proportional to d_-2.4 times a nearly periodic function of d, where d is the distance between two CDWs.