Small-$q$ Anomaly in the Dielectric Function and High-Temperature Oscillations of Screening Potential in 2D Electron Gas with Spin-Orbit Coupling

We study the static dielectric function $\epsilon(q)$ of 2D electron system with spin-orbit coupling in the frame of the random phase approximation. We demonstrate that, in addition to the well-known $2k_F$-Kohn anomaly, spin-orbit coupling gives rise to the novel anomaly in the dielectric function at small $q=q_0\ll k_F$, where $q_0$ is the distance between two Fermi surfaces. As a result of this anomaly a large-distance behavior of the potential from a point charge exhibits (in addition to the conventional Friedel oscillations) novel oscillations with a period $2\pi/q_0$. The remarkable feature of these oscillations is that they are not smeared out by the temperature. We show that the small-$q$ anomaly also modifies the indirect exchange interaction of localized magnetic moments (RKKY interaction). In the presense of spin-orbit coupling this interaction acquires a high-temperature component.