Interaction Effects in a High-Mobility Two-Dimensional Electron Gas in a Nonquantizing Magnetic Field

Two dimensional electron gas in a perpendicular nonquantizing magnetic field, $B$, is considered. We demonstrate \footnote{preprint cond-mat/0611111.} that the anomaly in the polarization operator, $\Pi(q)$, near $q=2k_F$, where $k_F$ is the Fermi momentum, gets smeared with $B$ in a peculiar fashion: slowly decaying modulation, periodic in $(2k_F-q)^{3/2}$, emerges. The period of modulation sets a spatial scale, $p_0^{-1}\propto B^{-2/3}$, which is much smaller than the Larmour radius, but much larger than the de Broglie wavelength. This scale manifests itself, {\em e.g.,} in lifting the periodicity of the Friedel oscillations, $\delta \rho (r)$ in magnetic field, namely we find that $\delta \rho (r)\propto \sin \left[2 k_F r-(p_0 r)^3/12\right]/r^2$. The corrections to the interaction-induced characteristics of the $2D$ gas, such as relaxation rate and the tunnel density of states, coming from the distances $\sim p_0^{-1}$, are shown to be strongly singular (as $B^{1/3}$) in magnetic field.