Spin dynamics of negatively charged excitons in CdSe/CdS colloidal nanocrystals

The spin dynamics in chemically synthesized CdSe/CdS core/shell nanocrystals (NCs) are studied by polarization- and time-resolved photoluminescence (PL) techniques in high magnetic fields and at low temperatures. Analysis of the recombination dynamics shows that the emission of thin-shell NCs is contributed by neutral excitons, while for thick-shell NCs it is dominated by charged excitons (trions). The sign of the PL polarization unambiguously demonstrates that these trions are negatively charged. A theoretical model of the PL polarization in an ensemble of randomly oriented NCs describes well magnetic field and time dependences of the PL polarization degree and allows us to determine the hole $g$ factor in CdSe/CdS NCs, $g_h=-0.54$. From direct measurements of the spin relaxation rate dependences on magnetic field and temperature, we identify the mechanism of the negative trion spin relaxation as two-phonon-assisted Raman scattering between the hole spin sublevels mixed by the applied magnetic field.

Figure 1

(a) Transmission electron microscopy image of 2.5/10 CdSe/CdS colloidal NCs. The image was taken on a JEOL 2010 field electron gun microscope operated at 200 keV. (b) PL spectra of thin-shell (2.5/2) and thick-shell (2.5/10) CdSe/CdS NCs under CW excitation.

Figure 2

(a), (b) Energy level schemes of neutral excitons and negative trions. $|A\rangle$, $|F\rangle$, and $|G\rangle$ denote bright exciton, dark exciton, and ground states, respectively. $\Delta E_{AF}$ is the bright-dark splitting. ${\gamma }_0$ is the spin relaxation rate from the bright to the dark exciton state. ${\gamma }_0{N}_B$ is the spin relaxation rate between bright and dark exciton states induced by thermal mixing. ${\Gamma }_A$ and ${\Gamma }_F$ are recombination rates of bright and dark excitons. $|\pm \frac{1}{2}\rangle$ and $|\pm \frac{3}{2}\rangle$ are negative trion states with $M=\pm \frac{1}{2},\pm \frac{3}{2}$. $|G,e\rangle$ is the ground state of the negative trion, which is a resident electron in the CdSe core. $\Delta E_{LH}$ is the splitting between heavy hole and light hole. (c), (d) Temperature dependences of normalized PL decay of CdSe/CdS NCs with shell thicknesses of 2 and 10 nm at $B=0$ T. Insets: normalized PL decay at $B=0$ and 15 T for $T=4.2$ K.

Figure 3

(a) Polarized PL spectra of thick-shell $2.5$/10 CdSe/CdS NCs at $B=0$ and 15 T measured under CW excitation with 50 mW/cm${}^2$ power. Inset: Magnetic field dependence of the integral PL intensity summed over both polarizations ($I^{+}+I^{-}$). (b) Magnetic field dependences of the time-integrated DCP measured for CW (triangles and squares) and pulsed (circles) excitation on thick-shell 2.5/10 NCs. $T=4.2$ K.

Figure 4

Schematic presentation of the spin level structure and the optical transitions between these levels for negative and positive trions in an external magnetic field. Short black and orange arrows indicate electron and hole spins, respectively. Polarized optical transitions are shown by red (${\sigma }^{+}$) and blue (${\sigma }^{-}$) arrows. The more intense emission, shown by thicker arrow, comes from the lowest in energy trion state with spin $-\frac{3}{2}$ for the negative trion and with spin $-\frac{1}{2}$ for the positive trion.

Figure 5

Polarization-resolved PL decay and time-resolved DCP for thick-shell 2.5/10 CdSe/CdS NCs measured under pulsed excitation with density 0.1 mW/cm${}^2$.

Figure 6

Time-resolved DCP of thick-shell $2.5$/10 CdSe/CdS NCs: (a) at different magnetic fields and $T=4.2$ K, and (b) at different temperatures and $B=5$ T. Red lines are fits according to Eq. (5).

Figure 7

(a) Magnetic field dependences of the DCP rise time ${\tau }_s^{\exp }$ (red squares) and PL decay time ${\tau }_r$ (black circles) for the thick-shell 2.5/10 CdSe/CdS NCs. Black line shows the evaluated optimal spin relaxation time ${\tau }_s^{\mathrm{opt}}$ in NCs, which give the maximum contribution to the dynamical spin polarization. (b) Magnetic field dependences of the dynamical factors: ${\tau }_r/({\tau }_s^{\exp }+{\tau }_r)$ and ${\tau }_r/({\tau }_s^{\mathrm{opt}}+{\tau }_r)$ at $T=4.2$ K.

Figure 8

Magnetic field (a) and temperature (b) dependences of the ensemble spin relaxation time of trions ${\tau }_s^{\exp }$ (circles). Red lines are guides for the eye.

Figure 9

(a) Magnetic field dependences of the equilibrium DCP $P_c^{\mathrm{eq}}$ (open circles), and time-integrated DCP $P_c^{\mathrm{int}}$ (closed circles), measured for thick-shell 2.5/10 CdSe/CdS NCs at $T=4.2$ K. The red and blue lines show the results of calculations based on Eqs. (7) and (9), respectively, with $g_h=-0.54$. (b) Magnetic field dependences of the time-dependent DCP $P_c\left(t\right)$ measured for 2.5/10 CdSe/CdS NCs at time delays of $t=1,2,8$, and 100 ns. Solid lines show the results of calculations after Eq. (8).

Figure 10

Calculated magnetic field dependence of spin relaxation times: red squares for NCs with fastest spin relaxation rate ${\tau }_s(\theta ={90}^{\circ })$; and black squares for NCs, which give the maximum contribution to the dynamical spin polarization ${\tau }_s^{\mathrm{opt}}$. Blue line shows the magnetic-field-independent spin relaxation time in NCs oriented along magnetic field ${\tau }_s(\theta =0^{\circ })$. Red line shows the magnetic field dependence of ${\tau }_s(\theta ={90}^{\circ })$ calculated using Eq. (11) using fit parameters described in the text. Black line shows the polynomial approximation of the ${\tau }_s^{\mathrm{opt}}$ dependence on magnetic field.

Figure 11

Dependences of the ${\tau }_r/[{\tau }_s(B,x,T)+{\tau }_r]$, ${\rho }_0(B,x,T)$ and their product ${\rho }_s(B,x,T)$ on the angle $\theta$ (lower axes) and $x=\cos \theta$ (upper axes) calculated for $T=4.2$ K and $B=15$ T.

Figure 12

Temperature dependences of parameters $\alpha \left(T\right)$ (closed squares) and $1/{\tau }_{s0}\left(T\right)$ (open squares) that determine the spin relaxation time ${\tau }_s$ in thick-shell 2.5/10 CdSe/CdS NCs. Red and blue lines show temperature dependences calculated according to Eqs. (12) and (13), respectively. Calculations were done using activation energies of $E_{\alpha }=0.6$ meV and $E_0=0.2$ meV. Other fit parameters are given in text.

Figure 13

(a) Time-dependent DCP of CdSe/CdS NCs with shell thicknesses varying from 2 to 10 nm, NC core radius is 2.5 nm. (b) Dependences of DCP rise time ${\tau }_s^{\exp }$ on the shell thickness at magnetic fields $B=1,2$, and 3 T.