Determination of Rashba and Dresslhaus coefficient in InGaAs quantum wells*

We report the determination of the intrinsic spin-orbit interaction (SOI) parameters for In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells (QWs) from the analysis of the weak antilocalization effect measured at dilution temperature [1]. We found that the Dresselhaus SOI is mostly negligible relative to the Rashba SOI in this system. The intrinsic parameter for the Rashba effect, a$_{\rm SO}\equiv \alpha/\langle E_z \rangle$, is determined to be a$_{\rm SO}m^*/m_e = (1.46-1.51 \times 10^{-17}N_{\rm S}$ [m$^{-2}$]) $e${\AA}$^2$, where $\alpha$ is the Rashba SOI coefficient, $\langle E_z \rangle$ is the expected electric field within the QW, $m^*/m_e$ is the electron effective mass ratio, and $N_{\rm S}$ is the sheet carrier density. The $N_{\rm S}$ dependence of a$_{\rm SO}$ corrsponds to the non-parabolic correction in the effective mass or electron g-factor. These values for a$_{\rm SO}m^*$, which are in good agreement with the thoretical prediction by Kane's ${\bf k\cdot p}$ theory, were also confirmed by the observation of beatings in the Shubnikov-de Haas oscillations in our most asymmetric QW sample.\\[4pt] [1] S. Faniel {\it et. al.}, PHYSICAL REVIEW B {\bf 83}, 115309 (2011).