Main

The samples studied in this work are ensembles consisting of nanocrystals with a 5.5-nm-diameter, low-bandgap (Eg=1.74 eV) CdSe core, surrounded by a three-monolayer (ML), high-bandgap (Eg=3.68 eV) ZnS barrier and a 4 ML outer CdSe shell7. A cut-away illustration of the sample structure is shown in Fig. 1a. Qualitatively similar results were also obtained on a sample with 6.4 nm core, 2 ML barrier and 4 ML shell. For comparison, a control sample of 6.8-nm-diameter CdSe QDs was also prepared.

Figure 1: Sample characterization and selective pumping of the core and shell.
figure 1

a, Top: Cutaway illustration of a QDQW. Bottom: Schematic diagram of conduction- and valence-band profiles in the radial direction. Red (blue) lines show |r Ψ|2 in the lowest core (shell) state from k · p calculations. Dashed lines show the d-like (L=2) part of the hole wavefunction. b, QDQW PL with Epump=2.43 eV (red) and Epump=2.01 eV (black). The grey line shows QDQW absorption. Note that the bandgap increases by ∼80 meV at 5 K. c, TA spectrum at fixed delay of 20 ps for CdSe QDs (left panel) and QDQWs (right panel). Epump=2.03 eV (black) and 2.30 eV (red). The inset shows the time dependence of the TA signal for CdSe QDs at Eprobe=2.03 eV. Black triangles show the two lowest calculated core and shell transition energies, 2.010 and 2.254 eV, respectively.

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Figure 1a shows the radial potential of the core–shell structure along with the conduction- (c-) and valence- (v-) band states, 1Se, 2Se, 1S3/2 and 2S3/2 (discussed below). The band profile is analogous to a pair of coupled quantum wells, in which the core corresponds to one well and the shell to the other. Indeed, under 2.43 eV excitation the photoluminescence (PL) spectrum of these quantum-dot quantum wells (QDQWs) (Fig. 1b) shows two peaks at 2.18 and 1.92 eV, which have been previously attributed to radiative recombination from an electron–hole pair in the shell and in the core, respectively7. When the excitation energy is tuned between the core and shell emission to 2.02 eV, only the lower-energy (core) emission is observed. This behaviour of the PL indicates that two optically active, metastable exciton states exist in the QDQWs, and that by changing the pump energy either the core or both the core and the shell can be selectively excited.

We have modelled the electronic states of the coupled core–shell QDQWs within k · p theory, extending our previous model of a single QDQW8,9. (The theoretical modelling is discussed in more detail in the Supplementary Information.) Although such a model is not rigorously applicable to structures with layers of only a few monolayers, we find that it still provides a surprisingly accurate description of the observed spectra. The calculated radial probability densities (|r Ψ|2) are shown in Fig. 1a for the two c-band states, 1Se (red) and 2Se (blue), and the two v-band states, 1S3/2 (red) and 2S3/2 (blue), for radii r1=2.75 nm, r2=3.68 nm and r3=5.08 nm. Here, we have applied the standard notation n Le and n LF for electron and hole states, as in refs 811. It is clear from Fig. 1a that the electron and hole are localized mainly in the core of the QDQW for the 1Se–1S3/2 exciton, and mainly in the shell for the 2Se–2S3/2 exciton. This latter state is the energetically lowest state with the electron and hole strongly localized in the shell. We therefore assign these two states to the core and shell PL peaks.

The wavefunctions and energy spectra vary significantly when changing the radii ri. We obtain fairly good agreement by comparing the calculated energies of the lowest core and shell states with the PL data in ref. 7 for several sets of ri reported in that work; see Fig. 4a,b. This indicates that the k · p model we apply here reasonably describes the size-dependent trends of the experimentally observed low-lying exciton energies.

Figure 4: Comparison with k · p theory and Hubbard model.
figure 4

a,b, Measured (circle) and calculated (star) core (red) and shell (blue) PL energies for QDQWs with varying shell thickness (a) and core diameter (b). c, Radial wavefunctions of the lowest c-band core state (left) and shell state (right) calculated for the coupled core–shell structure (black) and calculated using a two-site Hubbard model (red).

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We use transient absorption (TA) measurements to probe the carrier dynamics in these QDQWs. Here, a pump pulse excites carriers within the QDQWs, and a spectrally broad probe pulse then measures the change in the optical absorption spectrum induced by the pump. The left panel of Fig. 1c shows the TA spectrum from the CdSe QD control sample at a fixed pump–probe delay of 20 ps, with a pump energy of 2.30 eV (red) and 2.03 eV (black). Two effects contribute to the observed spectrum: strictly positive signal due to bleaching of interband transitions, and signal caused by shifts in the spectrum due to multiparticle effects12,13. This second effect results in both positive and negative contributions. The large peak at 2.05 eV is attributed to bleaching of the lowest optically active transition. It is apparent that the TA spectrum in the control sample is largely independent of pump energy. The time dependence of the TA signal at 2.03 eV up to the maximum pump–probe separation of 2.5 ns is shown in the inset of Fig. 1c, and is essentially the same in both samples at all energies at the timescales shown here.

The results of the same TA measurements made on the QDQW sample are shown in the right panel of Fig. 1c. At the low pump energy (2.03 eV), where only the core state is excited, the TA spectrum is very similar to the spectrum of the CdSe QDs. However, at higher pump energy (2.30 eV) a second large positive peak appears due to bleaching of transitions to the shell state. The black triangles in Fig. 1c indicate the calculated energies of the lowest core and shell transitions, 1Se–1S3/2 (2.010 eV) and 2Se–2S3/2 (2.254 eV), in reasonable agreement with the two bleaching peaks in the TA spectrum. This provides further confirmation that a second, higher-energy metastable (lifetime≫3 ns) state exists in the QDQWs. In fact, time-resolved PL measurements (not shown), made by time-correlated photon counting on QDQWs in toluene solution, show both core and shell states to have a room-temperature radiative lifetime of ∼20 ns, similar to previously measured radiative lifetimes in CdSe QDs14.

Using a circularly polarized pump pulse, we can excite spin-polarized carriers into these two metastable states, and then probe the resulting spin dynamics through time-resolved Faraday rotation (TRFR). A 2 T magnetic field is applied perpendicular to the pump and probe direction (Voigt geometry). The left column of Fig. 2 shows characteristic spin precession in the QDQW sample measured by TRFR at several pump and probe energies. The corresponding Fourier transforms (FTs) are shown in the right column. At this field, the spin lifetime is dominated by inhomogeneous dephasing due to the size and shape distribution of the nanocrystals. It has been previously observed for CdSe QDs15, as well as QDQWs with a single well9, that the spin dynamics show two distinct precession frequencies. The origin of these two precession frequencies (or g factors) is still unclear, though it has been suggested that one precession frequency may be due to lone-electron spins and the other to exciton spins15,16. It has been shown for CdSe QDs that the relative amplitude of the two precession components depends on the pump energy, but is essentially independent of the probe energy15. In the core–shell QDQWs, with the pump energy tuned to excite carriers only into the core (Epump=2.07 eV) as shown in Fig. 2a,b, two frequencies are observed with only small changes in their relative amplitude as the probe energy is varied. This is similar to the case in CdSe QDs. When pumping at higher energy, however, where both the core and the shell are excited, a significant change in the ratio of the two frequency components is observed with changing probe energy. Furthermore, a third precession frequency appears at high probe energy. All three of these frequencies vary linearly with the applied field, and they correspond to g factors of 1.34, 1.48 and 1.70.

Figure 2: Spin precession in core–shell QDQWs.
figure 2

TRFR scans (left column) and corresponding FTs (right column) on QDQWs at various pump and probe energies—data (black) and fits (red). We subtract a decaying exponential background before calculating the FTs. a–c, two-frequency fits. d, Three-frequency fit.

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For a more detailed look at the probe energy dependence of the spin dynamics, we passed the probe beam through a monochromator after the sample to narrow the probe linewidth to ∼5 meV, and TRFR measurements were made over a range of probe energies. The resulting curves of the Faraday rotation angle, θF, as a function of pump–probe delay, t, were normalized by the probe power and fitted by

where n=2 or 3 as needed to provide a good fit. The precession frequencies, ωi, and spin lifetimes, τi, were fixed for all the fits for a given probe energy scan, and the phases, φi, were approximately zero in all cases. The red curves in Fig. 2 show fits to the data. The origin of the non-oscillating components C and A0 is unclear and will not be discussed further here. The amplitudes Ai (i=1–3) correspond to the different frequency components seen in the FTs in Fig. 2. As was previously observed, in the CdSe QD control sample the ratio of amplitudes of the frequency components is largely independent of probe energy, though dependent on pump energy (Fig. 3a,b). Furthermore, the probe energy spectrum has essentially the same shape at both pump energies (though A1 is quite small at the higher pump energy). This is expected, as the carriers rapidly relax to the lowest exciton state12, regardless of pump energy.

Figure 3: Spectrally resolved spin dynamics in the core and shell.
figure 3

a–d, Fit parameters A1 and A2 (and A3 in d) from probe energy scans on the CdSe QD control sample (a,b) and the QDQW sample (c,d). Epump=2.03 eV (a,c) or 2.30 eV (b,d).

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As before, the QDQW sample shows similar behaviour to the control sample when only the core state is excited (Fig. 3c). However, when both the core and the shell are excited a third precession frequency appears only at high probe energy, as shown in Fig. 3d. The amplitude of Faraday rotation is a maximum for probe energies near interband transitions involving the occupied energy levels8. This probe energy dependence implies that the spins precessing at the third frequency are in a higher-energy state than those precessing at the other two frequencies. As the position of the third frequency peak corresponds to the higher-energy peak in the TA spectrum in Fig. 1c, it is reasonable to assign this precession frequency to electrons in the shell state.

On the basis of our calculated wavefunctions, we have estimated the effective g factor of the lowest core and shell c-band states by g=(pcore+pshell)gCdSe+pbarriergZnS+pvacgvac, where we have weighted the g factors in the CdSe, ZnS and surrounding vacuum with the probability pα for the electron to be in the region α (see the Supplementary Information). For the state 1Se, which is mainly localized in the core, we obtain g=1.04, and for the 2Se state, which is mainly localized in the shell, we obtain g=1.19. Although the difference of these two g factors is in good agreement with the two lowest measured g factors, the k · p model underestimates the absolute values of the g factors by about 20%. A more accurate theoretical description of these structures could be gained through detailed first-principles calculations17 or by taking into account interface terms18.

To obtain an estimate for the magnitude of the electron exchange interaction that may be expected in QDQW structures, we compare our theoretical results for the conduction band states, 1Se and 2Se, of the core–shell structure with a two-site Hubbard model to determine the tunnelling matrix element between the core and the shell. Here, we consider the ground state of a CdSe core surrounded by a ZnS barrier and the ground state of a CdSe shell enclosing a ZnS core, with energy difference Δ and coupled by a tunnelling matrix element tc (details given in Supplementary Information). We obtain Δ=143.3 meV and |tc|=30.7 meV. The Hubbard model reproduces the energies E 1 S e =0.2188 eV and E 2 S e =0.3727 eV with an accuracy of the order of a few meV. Good agreement is also obtained with the 1Se and 2Se wavefunctions calculated in the coupled core–shell model (see Fig. 4c). Further, the exchange interaction of two electron spins located in the core and the shell, respectively, can be estimated in the Hubbard model by ∼tc2/Δ∼1 meV for the present structure, as Δ is larger than the Coulomb repulsion (see the Supplementary Information). We note that the synthesis of QDQWs with small Δ might therefore provide an interesting basis to study interacting spins in coupled nanostructures.

Methods

Sample preparation

We synthesize the CdSe cores through standard colloidal chemistry19,20. We add subsequent layers onto the cores by successively alternating cation- and anion-containing solutions21. Transmission electron microscopy images show that the nanoparticles are fairly uniform in shape and size and are roughly spherical, with some faceting at the surface7. We disperse the QDQWs in a drop-cast polyvinylbutyral matrix and mount them in a magneto-optical cryostat for measurements at T=5 K. We purchased the CdSe QDs for the control sample, with peak emission at 5 K=2.03 eV, from Evident Technologies.

Time-resolved measurements

To make time-resolved measurements of the spin and carrier dynamics in these QDQWs (TRFR and TA, respectively), we use two optical parametric amplifiers seeded and pumped by an amplified Ti:sapphire laser. This allows pump–probe spectroscopy using two independently tunable, ∼200 fs duration pulses (∼30 meV linewidth), in addition to a white-light continuum. We focus the output of one optical parametric amplifier on the sample as a pump pulse (∼50 μm diameter, 0.5–1.0 mW), and overlap the output of the other optical parametric amplifier or the white light with the pump to serve as a probe pulse, which we delay in time using a mechanical delay line.

For TA measurements, we use the white light as the probe. After the probe passes through the sample, we disperse it in a 0.5 m spectrometer and detect it with a photomultiplier tube. By mechanically chopping both the pump and probe beams at different frequencies, f1 and f2, we can use lock-in detection at the sum frequency, f1+f2, to isolate the TA signal.

To excite spin-polarized electrons into the QDQWs, we modulate the pump-beam polarization between right and left circular polarization using a photoelastic modulator. As the linearly polarized probe pulse passes through the sample, its polarization rotates through an angle proportional to the spin polarization, owing to the Faraday effect. We measure the polarization rotation by a balanced photodiode bridge, and use lock-in detection at both the photoelastic-modulator frequency and the frequency of the mechanically chopped probe beam to isolate the pump-induced spin-polarization signal.