Energy Relaxation in the Spin-Polarized Disordered Electron Liquid

Abstract

Energy relaxation is studied in the spin-polarized disordered electron systems in the diffusive regime. We derive a quantum kinetic equation in which the kernel of the electron-electron collision integral explicitly depends on the electron magnetization. As a consequence, the inelastic scattering rate has a nonmonotonic dependence on the spin polarization of the system.

Keldysh technique and non-linear σ-model: basic principles and applications

“…Indeed, one may verify this statement explicitly by expanding the partition function (117) in powers of V cl and employing the Wick theorem. For example, in the first order, one finds Z[V cl , 0] = 1+ dt Tr γcl Ĝ(t, t) = 1, where one uses that γcl = 1 along with (105). It is straightforward to see that for exactly the same reason all higher-order terms in V cl vanish as well.…”

“…(v) Finally, the present discussion can be generalized to include a spin degree of freedom. Corresponding kinetic equation and collision kernel were obtained in [104,105].…”

Nonuniversal shot noise in quasiequilibrium spin valves

“…15 The role of e-e scattering is to equilibrate the electron system into a common local temperature without any transfer of electron energy to nonelectronic excitations. However, whereas in the absence of spin-flip scattering the spin-dependent potentials are unaffected by e-e scattering, the energies of the two spin ensembles are coupled, 9,[16][17][18] and therefore in the limit of strong e-e scattering spin-up and spin-down electrons can be described with the same temperature T (x).…”

Electron–electron interaction induced spin thermalization in quasi-low-dimensional spin valves

“…Moreover, it was pointed out in Refs. [5,6] that the electron-electron contribution to the energy relaxation in reduced dimensions diverges. In this paper we have addressed this divergence by introducing a natural cutoff emerging from the sample size.…”

“…When one or more of the dimensions are smaller than the thermal coherence length ξ T = D/(k B T ), the kernel of the electron-electron collision integral should be calculated for reduced (1D or 2D) spatial dimensions. In these cases the thermalization rate formally diverges [5,6] and needs to be properly regularized. In this paper we discuss such regularization schemes and calculate the resulting thermalization rates.…”