Experimental Separation of Rashba and Dresselhaus Spin Splittings in Semiconductor Quantum Wells

The relative strengths of Rashba and Dresselhaus terms describing the spin-orbit coupling in semiconductor quantum well (QW) structures are extracted from photocurrent measurements on $n$-type InAs QWs containing a two-dimensional electron gas (2DEG). This novel technique makes use of the angular distribution of the spin-galvanic effect at certain directions of spin orientation in the plane of a QW. The ratio of the relevant Rashba and Dresselhaus coefficients can be deduced directly from experiment and does not relay on theoretically obtained quantities. Thus our experiments open a new way to determine the different contributions to spin-orbit coupling.

Figure 1

Schematic 2D band structure with $\mathit{k}$-linear terms for ${\mathrm{C}}_{2v}$ symmetry for different relative strengths of SIA and BIA and the distribution of spin orientations at the 2D Fermi energy: (a) The case of only Rashba or Dresselhaus spin-orbit coupling. (d) The case of the simultaneous presence of both contributions. Arrows indicate the orientation of spins.

Figure 2

Angular dependence of the spin-galvanic current (a) and the geometry of the experiment (b),(c).

Figure 3

Photocurrent in $n$-type InAs single QWs. Left plates indicate three selected relations between spin polarization and current contributions [after Eq. (2)]. Right plates show measurements of the spin galvanic current as a function of angle $\Theta$. Data are presented in polar coordinates. The magnitude of the current measured at the radiation power of 10 kW is normalized to the current maximum ($j_{\max }=20\mu \mathrm{A}$) obtained in the geometry of (c).