Anomalous Hanle effect considered in time-resolved measurements and numerical simulations

In this study, the formation of a large in-plane nuclear field, known as the anomalous Hanle effect, in a self-assembled quantum dot was studied from both experimental and theoretical aspects. Time-resolved measurements of photoluminescence revealed that the buildup time of the nuclear field increased with increasing applied transverse magnetic field strength. Further, we found that inversion of the circular polarization degree of photoluminescence due to the excitation helicity reversal was completed on a timescale at least three orders of magnitude faster than the nuclear field buildup time. Accordingly, we reconsidered the previously proposed model for the anomalous Hanle effect. The alternatively developed model successfully explains the experimental results, suggesting that the in-plane component of the major principal axis of nuclear quadrupole interaction is essential for the generation of the anomalous Hanle effect.

Figure 1

Schematics of the measurement system. LP: linear polarizer. FM was used to switch between time-resolved and time-integrated PL measurements. The bottom panel shows the PL spectra obtained from a single QD ($E_{\mathrm{PL}}$: PL energy). A band-pass filter (BPF) allowed us to extract only $X^{+}$ PL peak as depicted in the inset.

Figure 2

(a) Time-integrated measurements of anomalous Hanle curves in a single InAlAs SAQD under ${\sigma }^{-}$ (blue) and ${\sigma }^{+}$ (orange) excitations. The dark (light) markers indicate the data obtained with increasing (decreasing) $B_x$. Hatched regions indicate the Hanle curves where $|{\mathit{B}}_{\mathrm{n}}|=0$. (b) ${\mathrm{\Delta }}_{\mathrm{OS}}$ as a function of $B_x$. Right axis corresponds $B_{\mathrm{n},z}$ deduced from $B_{\mathrm{n},z}={\mathrm{\Delta }}_{\mathrm{OS}}/\left({\mathrm{g}}_{\mathrm{e}}{\mu }_{\mathrm{B}}\right)$.

Figure 3

(a) Temporal evolutions of ${\rho }_{\mathrm{c}}$ with respect to the switching of excitation polarization ${\pi }^x\to {\sigma }^{\pm }$ at $t=0$. When $t>0$, blue and orange markers indicate data under ${\sigma }^{-}$ and ${\sigma }^{+}$ excitations, respectively. (b) $B_x$ dependence of $t_{\mathrm{buildup}}$. Blue (orange) squares indicate the case under ${\sigma }^{-(+)}$ excitation when $t>0$. (c) Temporal evolution of ${\rho }_{\mathrm{c}}$ with respect to the switching of excitation helicity; orange (blue) markers indicate the case with ${\sigma }^{-(+)}\to {\sigma }^{+(-)}$ at $t=0$. (d) The transition of ${\rho }_{\mathrm{c}}$ in the fast time range of $\left|t\right|<20\mu \mathrm{s}$ in the case of ${\sigma }^{+}\to {\sigma }^{-}$ at $t=0$. The data shown in (a), (c), and (d) were obtained at $B_x=0.5\mathrm{T}$.

Figure 4

Computed results of the dynamical changes in $\langle S_z\rangle , B_{\mathrm{n},x}$, and $B_{\mathrm{n},z}$ based on the previously proposed model [25]. $B_x$ was varied from 0 to 0.4 T. (a) and (b) depict the temporal evolutions of $\langle S_z\rangle$ (top panel), $B_{\mathrm{n},x}$ (middle), and $B_{\mathrm{n},z}$ (bottom) after the switching of ${\pi }^x\to {\sigma }^{-}$ and ${\sigma }^{-}\to {\sigma }^{+}$ at $t=0$, respectively. (c) The configuration of electron spin polarization $\langle \mathit{S}\rangle , {\mathit{B}}_{\mathrm{n}}$, and $B_x$. The left side shows the initial state in which $B_{\mathrm{n},z}$ begins to emerge, and the right side shows the final state in which $B_{\mathrm{n},x}$ that compensates for $B_x$ occurs. Here, ${\mathit{B}}_{\mathrm{T}}$ is a total effective magnetic field seen from the perspective of an electron, and $\langle {\mathit{S}}_0\rangle$ is the initial value of $\langle \mathit{S}\rangle$. (d) $B_x$ dependencies of $t_{\mathrm{buildup}}$ (squares) and $t_{\mathrm{dent}}$ (circles).

Figure 5

[(a) and (b)] Temporal evolutions of $\langle S_z\rangle$ (top) and $B_{\mathrm{n},x}$ (bottom) with respect to the switching of $({\pi }^x\to {\sigma }^{-})$ and $({\sigma }^{-}\to {\sigma }^{+})$, respectively. $B_x$ was varied from 0 to 0.3 T. In these computations, $I=3/2$ and $B_{\mathrm{Q}}=0.3\mathrm{T}$ are assumed. (c) $B_x$ dependence of $t_{\mathrm{buildup}}$ of $B_{\mathrm{n},x}$. Blue, orange, green, and red markers indicate the computed $t_{\mathrm{buildup}}$ of $B_{\mathrm{n},x}$ with $I=3/2, 5/2, 7/2$, and $9/2$, respectively. As shown in (a), the buildup time of $\langle S_z\rangle$ is in the same time scale. In these figures, the $q$ axes of all nuclei are assumed to be contained in the $xy$ plane.

Figure 6

Two limits of the major principal axis of NQI. (a) The $q$ axes of all nuclei in a QD are along the $z$ axis. (b) The $q$ axes of individual nuclei are in the $xy$ plane and uniformly distributed around the $z$ axis.

Figure 7

The computed results of $\langle S_z\rangle$ (top), $B_{\mathrm{n},x}$ (middle), and $B_{\mathrm{n},z}$ (bottom) in the steady state of the system. Here, a $q$ axis along $z$ is assumed. Solid and dotted curves correspond to the results with increasing and decreasing $B_x$, respectively. (a) Dependencies on NQI strength $B_{\mathrm{Q}}$ for $I=3/2$, where $B_{\mathrm{Q}}$ was varied from 0.0 to 1.5 T. (b) Difference in $I$ from $3/2$ to $9/2$ at a constant $B_{\mathrm{Q}}=1.5\mathrm{T}$.

Figure 8

The computed results of $\langle S_z\rangle$ (top), $B_{\mathrm{n},x}$ (middle), and $B_{\mathrm{n},z}$ (bottom) in the steady state of the system. The $q$ axes for all nuclei are contained in the $xy$ plane. Solid and dotted curves correspond to the results with increasing and decreasing $B_x$. (a) Dependencies on NQI strength $B_{\mathrm{Q}}$ on the computations for $I=3/2$. $B_{\mathrm{Q}}$ was varied from 0.1 to 1.0 T. (b) Difference in $I$ from $3/2$ to $9/2$ at a constant $B_{\mathrm{Q}}=0.1\mathrm{T}$.

Figure 9

The computed results of $\langle S_z\rangle$ (a), $B_{\mathrm{n},x}$ (b), and $B_{\mathrm{n},z}$ (c) in the steady state of the system under various values of the polar angle ${\theta }_{\mathrm{Q}}$ of the NQI major principal axis. Solid and dashed lines denote the results for increasing and decreasing $B_x$, respectively. All nuclei are assumed to have a spin of $3/2$, for simplicity.