Spin and orbital mechanisms of the magnetogyrotropic photogalvanic effects in GaAs/Al${}_x$Ga${}_{1-x}$As quantum well structures

We report on the study of the linear and circular magnetogyrotropic photogalvanic effect (MPGE) in GaAs/AlGaAs quantum well structures. Using the fact that in such structures the Landé factor $g^{*}$ depends on the quantum well (QW) width and has different signs for narrow and wide QWs, we succeeded to separate spin and orbital contributions to both MPGEs. Our experiments show that, for most QW widths, the MPGEs are mainly driven by spin-related mechanisms, which results in a photocurrent proportional to the $g^{*}$ factor. In structures with a vanishingly small $g^{*}$ factor, however, linear and circular MPGE are also detected, proving the existence of orbital mechanisms.

Figure 1

Conduction band structure of the samples.

Figure 2

(a) PL (dashed line) and PLE (solid line) spectra of sample E (15-nm wide QW). The arrow indicates the transition energy of the ($e2$-$\mathit{hh}2$) transition observed in the PLE spectrum. (b) PL peak energy as a function of the QW width. The dotted line indicates the transition energy for which the electron $g^{*}$ factor changes its sign.[35] (c) Energy difference between ($e1$-$\mathit{hh}1$) and ($e2$-$\mathit{hh}2$) transitions as a function of the QW width.

Figure 3

(a) TRKR traces measured on three different samples ($L_{\mathrm{QW}}=$ 4, 8, and 30 nm) with an applied in-plane magnetic field of 4 T. (b) Electron $g^{*}$ factor as a function of the QW width extracted from the TRKR data. The sign of the $g^{*}$ factor, which cannot be directly extracted from the TRKR traces, has been inferred from the PL transition energies.

Figure 4

(a) Zero-field TRKR traces measured on three different samples with $L_{\mathrm{QW}}=$ 4, 6, and 15 nm. (b) Zero-field SDT as a function of the QW width (log. scale). (c) ${\Omega }^2$ as a function of the QW width.

Figure 5

Dependence of the linear MPGE (circles) on $L_{\mathrm{QW}}$ obtained at room temperature, $B_y=\pm 1$ T and photon energy $\hslash \omega =4.4$ meV and corresponding $g^{*}$ factors (triangles, by TRKR). The inset shows the experimental geometry for the LMPGE.

Figure 6

Spin-based model for the linear MPGE. See details in the text.

Figure 7

Orbital model for the linear MPGE. Solid and dashed lines show the electron wave function with and without radiation, respectively.

Figure 8

Dependence of the spin-dependent and orbital contributions to the MPGE on the QW width.

Figure 9

Helicity dependence of the MPGE obtained for sample A at room temperature, $\left|B\right|=1$ T and a photon energy of $\hslash \omega =4.4$ meV. The ellipses on top illustrate the polarization states for various angles of the $\lambda /4$ plate, $\phi$. The inset depicts the spin-galvanic effect.

Figure 10

Dependence of the circular MPGE (squares) on $L_{\mathrm{QW}}$ obtained at room temperature, $\left|B\right|=1$ T and a photon energy of $\hslash \omega =4.4$ meV and corresponding $g^{*}$ factors (triangles, by TRKR). The inset shows the experimental geometry for the CMPGE.