Diamagnetic and paramagnetic shifts in self-assembled InAs lateral quantum dot molecules

We uncover the underlying physics that explains the energy shifts of discrete states of individual InAs lateral quantum dot molecules (LQDMs) as a function of magnetic fields applied in the Faraday geometry. We observe that ground states of the LQDM exhibit a diamagnetic shift while excited states exhibit a paramagnetic shift. We explain the physical origin of the transition between these two behaviors by analyzing the molecular exciton states with effective mass calculations. We find that charge carriers in delocalized molecular states can become localized in single QDs with increasing magnetic field. We further show that the net effects of broken symmetry of the molecule and Coulomb correlation lead to the paramagnetic response.

Figure 1

(a) Schematic band diagram of a single LQDM. The middle inset shows the cross-sectional profile of a single LQDM with arrows denoting the molecular axis and the direction of applied electric and magnetic fields. (b) PL from LQDM ensemble (blue), single LQDM GSs (black), and single LQDM ES1s (red) measured in flat-band conditions with zero magnetic field. The ensemble PL is fitted by four Gaussian curves (dashed lines) to identify four PL energy shells.

Figure 2

(a) Dependence of photoluminescence intensity of discrete spectral lines emitted from LQDMs excited by a laser with power ranging from 50 to 225 W/${\mathrm{cm}}^2$. The PL peak labels correspond to discrete ground (b) or excited (c) states evident in the line spectra.

Figure 3

(a) Energies of typical PL lines (GS, ES1) from two representative LQDMs as a function of magnetic field. (b) Diamagnetic coefficients for discrete PL lines from different energy shells of LQDMs as a function of PL energy.

Figure 4

Electron (left panels) and hole (right panels) charge densities corresponding to the three relevant exciton states at $B=0$ T and $B=3$ T. Dashed line circumferences depict the characteristic length of the harmonic oscillators defining each QD calculated for the electron and hole states with the largest contribution in the exciton wave function.

Figure 5

(a) Exciton emission spectrum as a function of magnetic field. Black dots are used for GS1 and GS2, red dots for ES1, and gray dots for other nonrelevant exciton states. The size of the dots is proportional to the optical intensity. (b) The expectation values of Coulomb interaction (dashed) and linear-in-$B$ single-particle terms for a LQDM (solid black) and a QD (solid blue).

Figure 6

Angular momentum expectation value for the electron in a $p$-shell exciton of a single QD (red dots) and that of a quasidegenerate LQDM (blue dots). For the single QD $\hslash \omega =25$ meV. For the LQDM $\hslash {\omega }_L=23.5$ meV (left dot) and $\hslash {\omega }_R=25.0$ meV (right dot). The distance between QD centers is 35 nm.

Figure 7

Calculated exciton emission emission spectra (top row) and exciton charge densities (bottom row) of LQDMs with different degrees of degeneracy.