Figure 1

(Color online) Schematics of energy levels and degeneracies in the single-particle (left-hand side) and excitonic (right-hand side) pictures. Single-particle levels are labeled as $p_n$, where $p=e,h$ is the charge carrier and $n$ is the order of the level (increasing from 1 starting from the CBM upwards for $e$ and from the VBM downwards for $h$). $\times d$ indicates the degeneracy (including spin). The zero of the energy is set arbitrarily at the position of the VBM. Single-exciton levels $|1h,1e⟩$ are labeled according to the SP states from which they originate as $\left(h_n,e_m\right)$. The zero of the energy is at the ground state $|0h,0e⟩$ (i.e, the state with zero electrons and zero holes). In the case of InAs spherical NCs, the lowermost exciton manifold $\left(h_{1,2},e_1\right)$ originates from the SP states $h_{1,2}$ (VBM) and $e_1$ (CBM) and has therefore a total degeneracy of $4\times 2=8$. However exchange interaction splits it into a lower threefold-degenerate multiplet, a middle twofold-, and a higher threefold-degenerate multiplets, separated by energy gaps of the order of hundreds of $\mu \text{eV}$ (not shown). We find very little configuration mixing in our InAs spherical NCs, with most excitons receiving a contribution $\ge 99\%$ from a single electron-hole pair $\left(h_n,e_m\right)$. The arrows indicate intraband (short blue and cyan) and interband (long red) absorption processes.Reuse & Permissions

Figure 2

(Color online) Density of states calculated for three InAs NCs with $R=14.6$, 20, and $24.1\text{Å}$ using a broadening of 30 meV. The 40 (ten) uppermost (lowermost) states in the valence (conduction) band are included. The arrows indicate the positions of the DOS peaks which could correspond to the state assignment made in Ref. 2 (labels on the peaks).Reuse & Permissions

Figure 3

(Color online) Comparison between the charge densities of the four uppermost (lowermost) states in the valence (conduction) band in InAs NCs with small radii of $14.6\text{Å}$ and aspect ratio $L/D=1$ (dot) and 1.4 (rod). The cross-section contours are plotted on the (001) atomic plane with their intensity increasing from blue to red. The NC boundaries are represented by dashed lines.Reuse & Permissions

Figure 4

(Color online) Comparison of the energy spacings between our calculated DOS peaks (blue solid symbols—for labeling see Fig. 2) and the measured STM (groups of) peaks [empty symbols, digitally extracted from Fig. 3b of Ref. 2], as a function of the single-particle energy gap.Reuse & Permissions

Figure 5

(Color online) Calculated intraband transitions for InAs NCs with $R=24.1\text{Å}$. (a) and (c) illustrate the intraband conduction-to-conduction (C-C) and valence-to-valence (V-V) single-particle transitions, respectively; (b) the calculated intraband (excitonic) absorption spectrum at room temperature with two different broadening lines ($\Gamma =5$ and 50 meV). For $\Gamma =5\text{meV}$, the group of peaks $\beta$ is decomposed into the different contributions from the two uppermost valence-band states: the features relative to transitions originating from the VBM (VBM-1) are marked with a blue (magenta) line in (b), according to the color code of the corresponding arrows in panel (c).Reuse & Permissions

Figure 6

(Color online) Comparison of our calculated intraband transition energies (red solid diamonds and triangles) and interband E5-E1 and E3-E1 energy spacings (blue solid circles and squares) with the valence and conduction intersublevel transition energies measured by PIA (empty diamonds and triangles, digitally extracted from Fig. 2 of Ref. 5) and PLE [empty circles and squares, digitally extracted from Fig. 3b of Ref. 2], see text, plotted as a function of the single-particle energy gap $E_g$ (the same as in Fig. 4). The energies E1, E3, and E5 refer to the positions of the strongest peaks measured in absorption and are defined in Fig. 7 (and relative text).Reuse & Permissions

Figure 7

(Color online) (a) Interband V-C absorption spectrum for an InAs nanocrystal with $R=24.1\text{Å}$ calculated with linewidths $\Gamma =0$ (red line), 10 (black line), and 30 meV (green line). The corresponding transitions between single-particle energy levels are shown in (b) with arrows. The lowest allowed transition $\left(\alpha \right)$ is the transition from VBM-1 to CBM.Reuse & Permissions

Figure 8

(Color online) Calculated positions of the optical-absorption features, relative to the first strong absorption peak (E1), in InAs NCs with radii ranging from 14.6 to $30\text{Å}$. Panels (a) and (c) display the absorption spectra relative to E1 for the largest and smallest NCs, respectively, with linewidths $\Gamma$ of 10 (ideal, colored line) and 30 meV (experimental-like, blue line): peaks with $\Gamma =10\text{meV}$ contributing to the same broad peak with $\Gamma =30\text{meV}$ have the same color. (b) Positions of all the absorption peaks calculated with $\Gamma =10\text{meV}$ (squares) relative to the first bright exciton (E1) versus E1 for InAs quantum dots with effective radii of 14.6, 20, 21.7, 24.1, 25.8, 27.7, and $30\text{Å}$, compared with PLE data (black symbols, digitally extracted from Fig. 4 of Ref. 3). The color coding corresponds to that used in panels (a) and (c).Reuse & Permissions

Figure 9

(Color online) First three strong-exciton energies relative to the lowest bright-exciton energy plotted with respect to the lowest bright exciton position. In addition to the comparison with PLE data (digitally extracted from Fig. 4 of Ref. 3), our results are compared with the results of the tight-binding method (Ref. 8) as well as the multiband effective-mass model (Ref. 3).Reuse & Permissions