Quantum corrections to conductivity of disordered electrons due to inelastic scattering off magnetic impurities

We study the quantum corrections to the conductivity of the two-dimensional disordered interacting electron system in the diffusive regime due to inelastic scattering off rare magnetic impurities. We focus on the case of very different $g$ factors for electrons and magnetic impurities. Within the Born approximation for the inelastic scattering off magnetic impurities we find additional temperature-dependent corrections to the conductivity of the Altshuler-Aronov type. Our results demonstrate that the low-temperature transport in interacting disordered electron systems with rare magnetic impurities is more interesting than it was commonly believed on the basis of treatment of magnetic impurity spins as classical ones.

Figure 1

The diagrammatic representation of equations for the diffusive propagators ${\mathcal{D}}_p\left(i\omega \right)$ (a) and ${\mathcal{D}}_p^{\left(rj\right)}\left(i\omega \right)$ (b). The solid line stands for the electron Green's function averaged over potential disorder and with self-energy correction due to scattering off magnetic impurities. The dashed line denotes the scattering off the potential disorder. The wavy line stands for the inelastic scattering off magnetic impurities. The Matsubara energies $\varepsilon ,\omega$, and $\mathrm{\Omega }$ are assumed to satisfy the following conditions: $\varepsilon <0,\varepsilon +\omega >0,\varepsilon +\mathrm{\Omega }<0$, and $\varepsilon +\omega +\mathrm{\Omega }>0$.

Figure 2

The sketch of diagrams contributing to the Altshuler-Aronov corrections. The springlike line stands for the dynamically screened electron-electron interaction ${\left[{\mathcal{D}}_p^{\left(rj\right)}\left(i{\omega }_m\right)\right]}^{-1}{\tilde{\mathcal{D}}}_p^{\left(rj\right)}\left(i{\omega }_m\right)$. The other elements have the same meaning as in the previous figure.