### Generation of spin current by Coulomb drag

• Coulomb drag between two wires results from Coulomb repulsion between electrons in the different wires, it exists in the absence of tunneling between the wires. Typical experimental set-up involves two wires (or, two conducting layers). Current I1 is driven via the active wire while in the passive one one adjusts voltage V2 so that I2=0. Figure below illustrates this (borrowed from M. Pustilnik's talk).

• Drag resistance can be calculated by equating forces acting on electron in the passive wire.

• In 1D wires, and at very low temperature, processes with large momentum transfer (2kF) between the wires are the most important. They are most effective when wires have equal densities, n1 = n2, in which case the wires "lock up" into zig-zag pattern (inter-wire charge density wave).

• The wires are, however, seldom completely equal. In that case one can apply magnetic field in order to tune densities of up-spin and down-spin electrons in the different wires separately. Indeed, assume first that n1 < n2 so that momentum mismatch between the wires forbids formation of the zig-zag order. Applied magnetic field changes densities of up- and down-spins, and one can now match the density of, say, up-spin electrons in the active wire with that of down-spin electrons in the passive one. In fact, under this conditions one generates spin current in the second wire, I2s = I2,↑ - I2,↓ ≠ 0 even though the charge current is absent, I2 = 0.
• See Generation of spin current by Coulomb drag, M. Pustilnik, E. G. Mishchenko, and O. A. Starykh, Phys. Rev. Lett. 97, 246803 (2006) for many more details.

• Once tunneling between the wires is allowed, one needs to think of many more processes. A very interesting one, called Cooper scattering, transfers pairs of electrons between the wires: this process always conserves momentum, even when densities in the wires are very different. In a single, two-subband wire such a process can generate superconducting correlations between electrons, even though the interaction is purely repulsive:
Oleg A. Starykh, Dmitrii L. Maslov, Wolfgang Häusler, and Leonid I. Glazman, Gapped phases of quantum wires, - cond-mat/9911286; published in Low-Dimensional Systems: Interactions and Transport Properties, pp.37-78, T. Brandes (Editor), Lecture Notes in Physics No. 544, Springer, 2000.