Electron $g$-factor anisotropy in symmetric (110)-oriented GaAs quantum wells

We demonstrate by spin quantum beat spectroscopy that in undoped symmetric (110)-oriented GaAs/AlGaAs single quantum wells, even a symmetric spatial envelope wave function gives rise to an asymmetric in-plane electron Landé $g$-factor. The anisotropy is neither a direct consequence of the asymmetric in-plane Dresselhaus splitting nor a direct consequence of the asymmetric Zeeman splitting of the hole bands, but rather it is a pure higher-order effect that exists as well for diamond-type lattices. The measurements for various well widths are very well described within $14\times 14$ band $\mathbf{k}·\mathbf{p}$ theory and illustrate that the electron spin is an excellent meter variable for mapping out the internal—otherwise hidden—symmetries in two-dimensional systems. Fourth-order perturbation theory yields an analytical expression for the strength of the $g$-factor anisotropy, providing a qualitative understanding of the observed effects.

Figure 1

Measured electron $g$-factor for the 12-nm, $(110)$-oriented, GaAs/Al${}_{0.32}$Ga${}_{0.68}$As, single QW in dependence on the angle $\phi$ between the $[1\overline{1}0]$ in-plane axis and the in-plane magnetic field orientation ($B=6$ T, $T=20$ K).[25] The line is a fit to the data according to Eq. (2) with $g_s=-0.212$, $g_a=+0.023$, and $\varphi =6.96$ mrad.

Figure 2

Measured $g$-factors (squares) in dependence on the angle $\phi$ for all ten QWs. The applied magnetic field is 6 T and the sample temperature 20 K. Note that the depicted values and curves are not shifted and all values correspond to the left axis. Calculations are with a $14\times 14$ $\mathbf{k}·\mathbf{p}$ model and a single common parameter set (solid lines).

Figure 3

The fitting values of $g_s$ (left) and $g_a$ (right) as a function of well width (squares). Calculations by a $14\times 14$ Hamiltonian (solid lines), by a simplified $2\times 2$ Hamiltonian using fourth-order Löwdin perturbation theory (dashed lines).