Gate control of low-temperature spin dynamics in two-dimensional hole systems

We have investigated spin and carrier dynamics of resident holes in high-mobility two-dimensional hole systems in $\text{GaAs}/{\text{Al}}_{0.3}{\text{Ga}}_{0.7}\text{As}$ single-quantum wells at temperatures down to 400 mK. Time-resolved Faraday and Kerr rotation as well as time-resolved photoluminescence spectroscopy are utilized in our study. We observe long-lived hole-spin dynamics that are strongly temperature dependent, indicating that in-plane localization is crucial for hole-spin coherence. By applying a gate voltage, we are able to tune the observed hole $g$ factor by more than 50%. Calculations of the hole $g$ tensor as a function of the applied bias show excellent agreement with our experimental findings.

Figure 1

(Color online) (a) Schematic growth layer sequence of the sample structures. (b) Corresponding one-dimensional band-structure profile along the growth direction. The red line schematically indicates the probability distribution of the hole wave function along the growth direction.

Figure 2

(Color online) (a) PL traces of sample A for different excitation powers. The PL measurements have been performed at a sample temperature of 1.2 K. The excitation power density has been varied between $3.8\text{mW}/{\text{cm}}^2$ and $95\text{W}/{\text{cm}}^2$. (b) Time-resolved PL traces of sample B taken at low excitation power (excitation density $6.4\text{W}/{\text{cm}}^2$). for sample temperatures of 4.5 (red circles) and 1.2 K (black squares).

Figure 3

(Color online) (a) TRFR traces of sample A for different sample temperatures. A 10 T in-plane magnetic field has been applied during the measurements. (b) Fourier transform amplitudes of the data from (a). (c) Frequency dispersion of electron (black dots) and hole (red open circles) spin precession as a function of the in-plane magnetic field. The measurements have been performed on sample A at a temperature of 1.2 K.

Figure 4

(Color online) Contour plot of gate-dependent PL measured on sample B. The PL measurements have been performed at a sample temperature of 4.5 K using an excitation density of $65\text{W}/{\text{cm}}^2$.

Figure 5

(Color online) (a) TRKR traces of sample B for different applied gate voltages, measured with an in-plane field of 6 T. (b) Kerr rotation amplitude of electron-spin precession at a fixed time delay as a function of the applied gate voltage, determined from the traces shown in (a). (c) Electron-spin lifetime as a function of the applied gate voltage.

Figure 6

(Color online) (a) TRKR traces of sample B for different applied gate voltages, measured with an in-plane field of 6 T. The gray arrow traces the position of the first hole-spin precession maximum. (b) Effective hole $g$ factor as a function of the applied gate voltage, determined from the traces shown in (a). The inset shows the definition of the hole $g$ factor components and the magnetic field angle with respect to the QW plane.

Figure 7

(Color online) (a) Calculated in-plane $\left(g_{\perp }\right)$ and growth-direction $\left(g_{\parallel }\right)$ hole $g$ factors as a function of the applied gate bias. (b) Effective hole $g$ factor resulting from Eq. (2), for the magnetic field lying either in-plane (blue line) or tilted by $7.5°$ with respect to the sample plane (red line). For comparison, we also show the experimental data points (black open circles).