Impurity effects in quantum dots: Toward quantitative modeling

We have studied the single-electron transport spectrum of a quantum dot in $\mathrm{GaAs}∕\mathrm{AlGaAs}$ resonant tunneling device. The measured spectrum has irregularities indicating a broken circular symmetry. We model the system with an external potential consisting of a parabolic confinement and a negatively charged Coulombic impurity placed in the vicinity of the quantum dot. The model leads to good agreement between the calculated single-electron eigenenergies and the experimental spectrum. Furthermore, we use the spin-density-functional theory to study the energies and angular momenta when the system contains many interacting electrons. In the high magnetic field regime the increasing electron number is shown to reduce the distortion induced by the impurity.

Figure 1

Sketch of the heterostructure of our sample.

Figure 2

Top: $G(V,B)$ plot of the transport spectrum of our sample. Bottom: $I\text{−}V$ characteristics for $B=0\mathrm{T}$.

Figure 3

(a) Profile of the external potential used in the simulation. (b) Sketch of the expected configuration of the QD-impurity system.

Figure 4

Measured transport spectrum (repeated from Fig. 2) of a $\mathrm{GaAs}∕\mathrm{AlGaAs}$ QD and the calculated single-electron energies (dashed lines) corresponding to the model potential shown in Fig. 3a.

Figure 5

Lowest noninteracting single-electron eigenenergies calculated for an impurity-containing QD with (thick lines) and without (thin lines) the rounding of the edges. The dashed lines show the corresponding eigenenergies (lifted by $+14\mathrm{meV}$ for clarity) for a clean dot.

Figure 6

Calculated chemical potentials for a clean (dashed lines, lifted by $+14\mathrm{meV}$ for clarity) and impurity-containing (solid lines) quantum dot up to six electrons. The dotted lines denote the borders for the full spin polarization. The other spin-state domains are also marked above and below the curves corresponding to the clean and impurity-containing cases, respectively.

Figure 7

Total angular momentum and electron density distributions for a six-electron QD as a function of the impurity distance from the dot center. The solid and dashed curves correspond to the magnetic fields of 20 and $25\mathrm{T}$, respectively.

Figure 8

Magnetization of the (fully polarized) state of a six-electron quantum dot at the impurity distances $R=0$ (plus markers) and $5\mathrm{nm}$ (cross markers) with (solid curves) and without (dashed curves) the electron-electron interactions. The effective Bohr magneton ${\mu }_B^{*}=e\hslash ∕2m^{*}$.