Few-Electron Molecular States and Their Transitions in a Single InAs Quantum Dot Molecule

We study electronic configurations in a single pair of vertically coupled self-assembled InAs quantum dots, holding just a few electrons. By comparing the experimental data of nonlinear single-electron transport spectra in a magnetic field with many-body calculations, we identify the spin and orbital configurations to confirm the formation of molecular states by filling both the quantum mechanically coupled symmetric and antisymmetric states. Filling of the antisymmetric states is less favored with increasing magnetic field, and this leads to various magnetic field induced transitions in the molecular states.

Figure 1

(a) Gray log-scale plot of current as a function of $V_G$ and transverse $B$ field with $V_{\mathrm{SD}}=0.5\mathrm{mV}$ for device $A$. (b) Corresponding for device $B$. (c) Calculated Fock-Darwin spectrum of a single dot assuming $\hslash {\omega }_0=10\mathrm{meV}$.

Figure 2

(a) Numerical calculation for device $A$ with ${\Delta }_{\mathrm{SAS}}=10.3\mathrm{meV}$. The GSs (ESs) are shown by the solid (dotted) lines. Black and red, respectively, indicate configurations with no filled AS states or with one or more filled AS states. The boxes and arrows inside represent the S (or AS) states and the spins, respectively. (b) Gray log-scale plot of magnified $N=5–8$ current peaks for device $A$, derived from Fig. 1a, with $V_{\mathrm{SD}}=0.5\mathrm{mV}$ as a function of $V_G$ and transverse $B$ field. Solid, open, and blue triangles indicate GS transitions described in the text, kinks, and cusps, respectively.

Figure 3

(a) Numerical calculation for device $B$ with ${\Delta }_{\mathrm{SAS}}=3.1\mathrm{meV}$. The GSs (ESs) are shown by the solid (dotted) lines. Black and red, respectively, indicate configuration with no filled AS states or with one or more filled AS states. The boxes and arrows inside represent the S (or AS) states and the spins, respectively. (b) Relative spacing $\Delta E_{N+1,N}$ between two neighboring peaks for $N=1–4$ as a function of the in-plane $B$ field whose direction is perpendicular to current, measured for device $B$ at 1.5 K. The red lines are fitted to $\Delta E_{2,1}$, $\Delta E_{3,2}$, and $\Delta E_{5,4}$. (c) Color contour plot of $dI/d{V}_{\mathrm{SD}}$ intensity for $N=6–7$ current peaks for device $B$ as a function of $V_G$ and transverse $B$ field with $V_{\mathrm{SD}}=4\mathrm{mV}$. The white dotted lines are a guide for eye. The yellow triangles (open circle) indicate GS (ES) transitions.