Rashba and Dresselhaus spin splittings in semiconductor quantum wells measured by spin photocurrents

The spin-galvanic effect and the circular photogalvanic effect induced by terahertz radiation are applied to determine the relative strengths of Rashba and Dresselhaus band spin splitting in (001)-grown GaAs and InAs based two dimensional electron systems. We observed that shifting the $\delta$-doping plane from one side of the quantum well to the other results in a change of sign of the photocurrent caused by Rashba spin splitting while the sign of the Dresselhaus term induced photocurrent remains. The measurements give the necessary feedback for technologists looking for structures with equal Rashba and Dresselhaus spin splittings or perfectly symmetric structures with zero Rashba constant.

Figure 1

(Color) Schematic 2D band structure with $\mathit{k}$-linear terms for $C_{2v}$ symmetry for nonequal strength of SIA and BIA. (a) The energy $\epsilon$ as a function of $k_x$ and $k_y$, (b) the distribution of spin orientations at the 2D Fermi energy.

Figure 2

Spin-galvanic currents in an (001)-grown QW for in-plane average spin direction given by arbitrary angle $\Psi$ (a), SGE-I geometry (b), and SGE-II geometry (c) and (d). It is assumed that $\alpha >\beta >0$.

Figure 3

Geometry of CPGE measurements (a) and angular dependence of the CPGE current (b).

Figure 4

Geometry of SGE measurements under optical excitation and Hanle effect (a) and angular dependence of the SGE current (b).

Figure 5

Azimuthal dependences of spin-galvanic (a) and circular photogalvanic (b) photocurrents, $j\left(\theta \right)$. Data are obtained in an $n$-type InAs single QW (sample 1) applying SGE-I and CPGE-I geometries. The magnitude of the current measured at radiation power of $10\mathrm{kW}$ is normalized to the current maximum detected in the $y^{\prime }$ direction $[j_{\max }=j_{\mathrm{SGE}}(\mathit{S}\Vert x^{\prime })]$ for SGE and $[j_{\max }=j_{\mathrm{CPGE}}(\widehat{\mathit{e}}\Vert x^{\prime })]$, respectively. Bottom panels show geometries of corresponding experiments.

Figure 6

Azimuthal dependences of spin-galvanic photocurrent measured in $n$-type InAs single QW (sample 1) applying SGE-II geometries. The magnitude of the current measured at radiation power of $10\mathrm{kW}$ is normalized to the current maximum $[j_{\max }=j_{\mathrm{SGE}}(S\Vert x^{\prime })=20\mu \mathrm{A}]$ detected in the $y^{\prime }$ direction obtained in the geometry (a). Bottom panels show geometries of corresponding experiments.