Spin Coulomb drag in the two-dimensional electron liquid

Abstract

We calculate the spin-drag transresistivity r "#(T) in a two-dimensional electron gas at temperature T in the random-phase approximation. In the low-temperature regime we show that, at variance with the threedimensional low-temperature result @r "#(T);T2#, the spin transresistivity of a two-dimensional spin unpolarized electron gas has the form r "#(T);T2ln T. In the spin-polarized case the familiar form r "#(T)5AT2 is recovered, but the constant of proportionality, A, diverges logarithmically as the spin-polarization tends to zero. In the high-temperature regime we obtain r "#(T)52(\/e2)(p2Ry*/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 ln T singularity at low temperature is smaller, in the Coulomb-drag case, by a factor e24kFd, 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.