Electron density effect on spin-orbit interaction in [001] GaAs quantum wells

The spin-orbit interaction of two-dimensional (2D) electrons in semiconductor quantum wells gives rise to a variety of interesting transport and optical spin-dependent effects. In the GaAs/AlGaAs type heterosystems, this interaction consists of the isotropic Bychkov-Rashba term, which is absent in symmetric wells, and the anisotropic Dresselhaus term, reflecting the lattice symmetry. It is well-known that the first term can be controlled by electric fields in the growth direction: external or internal, induced by a charge density of 2D electrons. In this work we reveal that the 2D electron charge can substantially affect also the Dresselhaus interaction in symmetric quantum wells. Within the one-band electron Hamiltonian containing, together with the bulk Dresselhaus interaction, the two contributions to the Dresselhaus term from the quantum well interfaces, we show that the internal electric field from the 2D electron charge density can substantially renormalize the anisotropic spin-orbit interaction of 2D electrons. This effect may be important in quantitative studies of spin-dependent phenomena in quantum wells.

Figure 1

Regions of qualitatively different structure of 2DEG in QW as a function of QW width. Red line shows the maximum possible electron density in QW, blue line bounds the region of concentrations with only one electron subband populatred, green and violet lines bound the regions with two and three subbands populated, respectively. Roman numerals $\mathrm{I}, \mathrm{II}, \mathrm{III}$, and $\mathrm{IV}$ show the regions of the QW widths and the electron density where 2DEG populates 1, 2, 3, and more subbands, respectively.

Figure 2

Profiles of electrostatic potential (upper panels) and electron density (lower panels) for two QWs with large electron density: QW width 5 nm and total density $n_{\mathrm{tot}}=1.02\times {10}^{12}{\mathrm{cm}}^{-2}$ (left panels) and QW width 20 nm and total density $n_{\mathrm{tot}}=6.45\times {10}^{11}{\mathrm{cm}}^{-2}$ (right panels). Profile of uncharged QW is shown in thin dashed line, the electrostatic profile of charged QW $U\left(z\right)$ is shown in red line. Fermi level $E_F$ is shown in blue dashed horizontal line.

Figure 3

Bulk and interface contributions to the Dresselhaus constant $\beta$ as a function of electron density for quantum well width 5 nm (upper row) and 20 nm (second row). The values of the bulk contribution ${\beta }_b$ to the constant $\beta$ at zero 2D electron density $n_{\mathrm{tot}}=0$, are 19 $\mathrm{meV}$ Å for the 5-nm well and 3.8 $\mathrm{meV}$ Å for 20-nm well. Bottom panel shows the change of the total Dresselhaus constant $\beta \left(n_{\mathrm{tot}}\right)-\beta (n_{\mathrm{tot}}=0)$ as a function of electron density for few selected QW widths.