Spin Coulomb drag in the two-dimensional electron liquid

Irene D'Amico; Giovanni Vignale

doi:10.1103/PhysRevB.68.045307

paper

Spin Coulomb drag in the two-dimensional electron liquid

arXiv:cond-mat/0112294 · doi:10.1103/PhysRevB.68.045307

Abstract

We calculate the spin-drag transresistivity $ρ_{↑↓} (T)$ 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 three-dimensional low-temperature result [ $ρ_{↑↓} (T) \sim T^{2}$ ], the spin transresistivity of a two-dimensional {\it spin unpolarized} electron gas has the form $ρ_{↑↓} (T) \sim T^{2} ln T$ . In the spin-polarized case the familiar form $ρ_{↑↓} (T) = A T^{2}$ is recovered, but the constant of proportionality $A$ diverges logarithmically as the spin-polarization tends to zero. In the high-temperature regime we obtain $ρ_{↑↓} (T) = - (ℏ/ e^{2}) (π^{2} R y^{*} / k_{B} T)$ (where $R y^{*}$ is the effective Rydberg energy) {\it 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 $e^{- 4 k_{F} d}$ where $k_{F}$ 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.

6 figures; various changes; version accepted for publication

Spin Coulomb drag in the two-dimensional electron liquid

Abstract

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