Fine structure of a resonantly excited $p$-shell exciton in a CdTe quantum dot

We present a polarization-resolved photoluminescence excitation study of the absorption spectrum of a $p$-shell neutral exciton in a single CdTe/ZnTe quantum dot. We find that the fine structure of the $p$-shell exciton is completely analogous to the fine structure of the $s$-shell exciton, including the selection rules and the effects of a magnetic field applied in Faraday and Voigt configurations. The energy spectrum of the $p$-shell exciton is found to be well described by introducing respective isotropic and anisotropic constants of the exchange interaction between a $p$-shell electron and a $p$-shell hole. The typical values of these exchange constants averaged over several randomly selected quantum dots yield ${\delta }_0^{pp}=(0.92\pm 0.16)$ meV and ${\delta }_1^{pp}=(0.58\pm 0.25)$ meV. Additionally, we demonstrate that the nonresonant relaxation of the $p$-shell exciton conserves the exciton spin to a very high degree for both bright and dark exciton configurations.

Figure 1

(a) PL and PLE spectra measured for the same CdTe/ZnTe QD (the spectra are offset for clarity). The upper curve represents the PL spectrum measured under quasiresonant excitation with the use of excitation transfer from a spontaneously coupled QD. The lower curves correspond to the PLE spectrum of the neutral exciton and the PL spectrum excited resonantly at the ${\mathrm{X}}^{*}$ excited state (as indicated). Both of the PL spectra were corrected for residual background emission by subtracting a reference signal measured at different excitation energy detuned from the resonance. Similarly, the PLE spectrum was obtained after subtraction of a reference signal taken at emission energy corresponding to a flat PL background. (b) The energy splitting $\mathrm{\Delta }{E}_{{\mathrm{X}}^{*}}$ between ground and first excited neutral exciton states vs intershell splitting $\mathrm{\Delta }{E}_{sp}$ of $s$- and $p$-shell emission bands (each data point corresponds to a different QD). The solid line represents the linear fit, while the dashed line corresponding to $y=x$ dependence is drawn for the reference.

Figure 2

(a),(b) Polar plots showing the intensities of (a) the X PL lines measured for different orientations of linear polarization of detection and (b) the X PLE signal (integrated over both X emission lines) measured for different orientations of linear polarization of excitation tuned to the energies of two fine-structure-split ${\mathrm{X}}^{*}$ peaks. The sample was oriented according to the cleaving axes, i.e., the [100] direction corresponds to ${45}^{\circ }$. In both plots the PL or PLE intensities of low-energy (high-energy) components of X or ${\mathrm{X}}^{*}$ doublets are presented with open circles (full squares). Dashed lines schematically mark the orientations of linear polarizations of each transition. Note that in (b) the symbols for angles $\phi$ and $\phi +{180}^{\circ }$ correspond to the same data points. (c) The X PL spectra excited resonantly at low-energy (black) and high-energy (red or gray) ${\mathrm{X}}^{*}$ absorption lines. The spectra were measured without polarization resolution. (d) The corresponding unpolarized X PLE spectra detected at high-energy (black) and low-energy (red or gray) X PL lines. The two peaks visible in the spectra correspond to the two components of the ${\mathrm{X}}^{*}$ resonance. For the sake of the presentation, the intensities corresponding to different series of data in each panel (a–d) were normalized.

Figure 3

(a) A schematic illustration of the magnetic field evolution of ${\mathrm{X}}^{*}$ and X energy levels in the Faraday configuration. Dashed arrows mark the spin-conserving nonradiative excitonic relaxation from the excited ${\mathrm{X}}^{*}$ state towards the ground X state. (b) The energy splittings between the pairs of X and ${\mathrm{X}}^{*}$ states vs the magnetic field applied in the Faraday geometry. The solid lines represent the fitted curves described in the text. (c) The X PL spectra and (d) the corresponding X PLE spectra showing the ${\mathrm{X}}^{*}$ resonance measured without polarization resolution at $B=10$ T (the spectra were normalized for better visibility). The black curves represent the PL spectrum excited at the low-energy ${\mathrm{X}}^{*}$ line and the PLE spectrum detected at the low-energy X line, while the red (gray) curves correspond to the spectra obtained for the respective high-energy lines.

Figure 4

(a) The scheme of energy levels of bright and dark states of the X and ${\mathrm{X}}^{*}$ excitonic states. Dashed arrows mark the spin-conserving nonradiative relaxation of an excited exciton towards its ground state. (b) Color-scale plot presenting the PLE map of the neutral exciton measured without polarization resolution at the magnetic field of 5 T applied in Voigt geometry.