Spin-orbit coupling measurement by the scanning gate microscopy

We propose a procedure for extraction of the Fermi surface for a two-dimensional electron gas with a strong Rashba spin-orbit coupling from conductance microscopy. Due to the interplay between the effective spin-orbit magnetic field and the external one within the plane of confinement, the backscattering induced by a charged tip of an atomic force microscope located above the sample, leads to the spin precession, and thus to the spin mixing of the incident and reflected modes. This mixing leads to a characteristic angle-dependent beating pattern visible in the conductance maps. We show that the structure of the Fermi level, bearing signatures of the spin-orbit coupling, can be extracted from the Fourier transform of the interference fringes in the conductance maps as a function of the magnetic field direction. We propose a simple analytical model which can be used to fit the experimental data in order to obtain the spin-orbit coupling constant.