Longitudinal and transverse exciton-spin relaxation in a single InAsP quantum dot embedded inside a standing InP nanowire using photoluminescence spectroscopy

We have investigated the optical properties of a single InAsP quantum dot embedded in a standing InP nanowire. Elongation of the transverse exciton-spin relaxation time of the exciton state with decreasing excitation power was observed by first-order photon correlation measurements. This behavior is well explained by the motional narrowing mechanism induced by Gaussian fluctuations of environmental charges in the nanowire. The longitudinal exciton-spin relaxation time is evaluated by the degree of the random polarization of emission originating from exciton states confined in a single-nanowire quantum dot by using Mueller calculus based on Stokes parameters representation. The reduction in the random polarization component with decreasing excitation power is caused by suppression of the exchange interaction of electron and hole due to an optically induced internal electric field by the dipoles at the wurtzite and zinc-blende heterointerfaces in the InP nanowire.

Figure 1

Schematic of the experimental setup. First-order photon correlation measurements were performed by measuring the PL passing through a Mach-Zehnder interferometer (MZI). The photon count was displayed as a function of the optical path delay. Full polarization measurements (FPMs) were performed using a set of quarter-wave plate (QWP), half-wave plate (HWP), and linear polarizer (LP). The PL decay time constant was measured using a streak camera. LPF, long-wave-pass filter; FM, flipper-mounted mirror; PS, phase shifter; NPBS, nonpolarizing beam splitter; PA, photodiode array. Inset: Microscope image of the sample surface and schematic of the NW-QD grown on InP (111)A substrate.

Figure 2

(a) PL intensities of $X^0$ and $X{X}^0$ peaks as a function of excitation power. Red and blue lines are guides for the eye. (b) PL spectra of an InAsP NW-QD obtained under different excitation conditions. $X^0$ PL appears under two-color excitation $\left(\mathrm{I}\right)+\left(\mathrm{II}\right)$, which corresponds to the PL spectra under laser (I) high-power excitation at 1 $\mu$W. Excitation conditions are as follows: (I) a green 2.33-eV laser creates electrons and holes in an InP NW; (II) an NIR 1.35-eV laser creates excitons in an InAsP NW-QD. Laser powers are 10 nW (I) and 25 $\mu$W (II). Inset: Schematics energy band diagram. Graded areas in the InAsP QD schematic indicate continuum states. (c) Zeeman energy and diamagnetic shift of $X^0$. Filled (black) circles and open (red) circles represent experimental data, the (black) line and (red) curve are fits to the data with $|g_{\mathrm{ex}}|{\mu }_{\mathrm{B}}{B}_z$ and ${\gamma }_2{B}_z^2$, respectively. $|g_{\mathrm{ex}}|=0.4$ and ${\gamma }_2=23.2\pm 0.3$ $\mu$eV/T${}^2$. (d) Time-resolved PL of $X^0$ [filled (black) circles] under type (I; pulsed) excitation at 0.1 $\mu$W. The $X^0$ decay time of $\sim$2 ns is fitted with a single-exponential function [solid (black) line].

Figure 3

(a) Visibility plot for single-dot $X^0$ PL. Inset: Short-period fringe evolution of PL at a delay time of 10 ns. (b) Excitation power ($P$) dependence of $T_2$ [filled (red) circles] under He-Ne laser excitation, with the corresponding solid (red) curve representing the calculation results using Eq. (1), and the PL peak energy of $X^0$, $\Delta E=E\left(P\right)-E\left(2\mu \mathrm{W}\right)$ [filled (blue) circles]. The area between the dashed (red) curves indicates the calculation results of $T_2$ for $T_2^{\left(\mathrm{lp}\right)}=45\pm 5$ ps. The $P$ dependence of $T_2$ is calculated by the motional narrowing fluctuation for $T=6$–10 K [solid (gray) curves] under fixed phonon energies, $E_1\sim$1 meV and $E_2=42.4$ meV.

Figure 4

(a) 2D plot of normalized PL intensities of $X^0$ as a function of $\rho$ and $\theta$. (b) Mueller calculus' results by using the components $\{1,0.32,-0.6,0.14\}$. (c) Polar plot of the PL intensity of $X^0$. The detection angle ($2\rho$) dependence of $I_{\mathrm{PL}}({59}^{\circ },\rho )/\left\{2\mathcal{h}{I}_{\mathrm{PL}}^{{59}^{\circ }}\left(\rho \right)\mathcal{i}\right\}$ (open (red) circles). Solid (red) and dashed (blue) lines are Mueller calculus' results for $\alpha =0.3$, $\{1,0.32,-0.6,0.14\}$ and $\alpha =0$, $\{1,0.32/0.7,-0.6/0.7,0.14/0.7\}$, with the latter being perfectly coherent light with a fixed ratio of the three polarization components. All angles are measured in the same laboratory frame. (d) $\Delta E$-dependence of the DRP $\alpha$ under fixed ratios of Stokes parameters of the polarization components $\{S_1,S_2,S_3\}$.

Figure 5

Calculation results for ${\tau }_2$ vs. ${\tau }_1$ [filled (red) circles] and ${\tau }_3$ vs. ${\tau }_1$ [open (blue) circles]. The solid (red) curve is a fit using a square root function. The solid (blue) line is a fit using a linear function.