Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in presence of magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and gives rise to the beating patterns in the amplitude of the Shubnikov de Hass (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.