Beating of Friedel Oscillations in Spin-Orbit Coupled System

The interplay of different spin-orbit interaction mechanisms induces highly anisotropic modifications of the static dielectric function of a two-dimensional electron system. One of the main changes of the static polarization function is the induced shift of its singularity position, which is in opposite directions for orthogonal momentum orientations. More interestingly, we have found that in certain situations the polarization function exhibits a \textit{doubly-singula}r behavior. This new property generates a novel phenomenon--\textit{the beating of Friedel oscillation}s, which can be controlled by an external electric field. This effect is a general feature of systems with Bychkov-Rashba and Dresselhaus spin-orbit fields and should be directly observable through tunneling microscopy imaging of the density distribution around an impurity.