Spin Coulomb drag in the two-dimensional electron liquid

We calculate the spin-drag transresistivity ρ↑↓(T ) in a two-dimensional electron gas at temperature T in the random phase approximation. In the lowtemperature regime we show that, at variance with the three-dimensional low-temperature result [ρ↑↓(T ) ∼ T 2], the spin transresistivity of a twodimensional spin unpolarized electron gas has the form ρ↑↓(T ) ∼ T 2 lnT . In the spin-polarized case the familiar form ρ↑↓(T ) = AT 2 is recovered, but the constant of proportionality A diverges logarithmically as the spinpolarization tends to zero. In the high-temperature regime we obtain ρ↑↓(T ) = −(h̄/e)(πRy/kBT ) (where Ry is the effective Rydberg energy) independent of the density. Again, this differs from the three-dimensional result, which has a logarithmic dependence on the density. Two important differences between the spin-drag transresistivity and the ordinary Coulomb drag transresistivity are pointed out: (i) The lnT singularity at low temperature is smaller, in the Coulomb drag case, by a factor e−4kF d where kF is the Fermi wave vector and d is the separation between the layers. (ii) The collective mode contribution to the spin-drag transresistivity is negligible at all temperatures. Moreover the spin drag effect is, for comparable parameters, larger than the ordinary Coulomb drag effect. 72.25.-b, 72.10.-d, 72.25.Dc Typeset using REVTEX 1