Shell Filling and Paramagnetism in Few-Electron Colloidal Nanoplatelets

Colloidal semiconductor nanoplatelets are excellent optical emitters, which combine a quasi-2D structure with strong in-plane Coulomb interactions. Here, we go beyond the photoexcitation regime and investigate theoretically the effect of charging nanoplatelets with a few interacting fermions (electrons or holes). This introduces severe Coulomb repulsions in the system, enhanced by the inherent dielectric confinement. We predict strong electronic correlations and electron-electron exchange energies (over 20 meV) in type-I ($\mathrm{CdSe}/\mathrm{CdS}$) and type-II ($\mathrm{CdSe}/\mathrm{CdTe}$) nanoplatelets, which give rise to characteristic physical phenomena. These include shell filling spectra deviating from the Aufbau principle, large addition energies which permit deterministic control of the number of charges at room temperature and paramagnetic electron spin configuration activated at cryogenic temperatures.

Figure 1

(a) Schematic of the $\mathrm{CdSe}/\mathrm{CdS}$ NPLs under study. (b) Noninteracting electron (top) and hole (bottom) energy levels as a function of the core length. (c) Wave functions of the lowest electron (highest hole) energy levels for $L_y^c=20\mathrm{nm}$. (d)–(f): same but for $\mathrm{CdSe}/\mathrm{CdTe}$ NPLs. The NPLs have the same dimensions as for $\mathrm{CdSe}/\mathrm{CdS}$. All energies are referred to the top of the CdSe valence band. The colors of the lines in (b), (c), (e), and (f) denote the irreducible representation of the level (within the $D_{2h}$ point group).

Figure 2

Additional energy spectra as a function of the number of carriers for $\mathrm{CdSe}/\mathrm{CdS}$ (red line) and $\mathrm{CdSe}/\mathrm{CdTe}$ (gray line) in a NPL with $L_y^c=20\mathrm{nm}$. (a) Noninteracting electrons. (b) Interacting electrons neglecting dielectric confinement (${ϵ}_{\mathrm{out}}={ϵ}_{\mathrm{in}}$). (c) Interacting electrons including dielectric confinement (${ϵ}_{\mathrm{out}}=2$). (d)–(f) Same for holes. The insets show the dominant electronic configuration along with its weight in the CI expansion (red value for $\mathrm{CdSe}/\mathrm{CdS}$, gray one for $\mathrm{CdSe}/\mathrm{CdTe}$).

Figure 3

(a) Energy splitting between ground state (singlet) and the first excited state (triplet) for two electrons in $\mathrm{CdSe}/\mathrm{CdS}$ NPL with varying core length. The insets illustrate the main electronic configuration for each state. The dotted line in (a) represents the triplet state of two noninteracting electrons, for comparison. (b)–(d) Expectation value of total electron spin as a function of the temperature for different core lengths, with two (b), three (c), and four (d) electrons. $⟨S_e{⟩}_{\mathrm{eq}}$ is the value for an equal number of low and high spin states populated. Solid (dashed) lines are used for calculations including (excluding) dielectric confinement.