Far-infrared absorption of vertically coupled self-assembled quantum rings

We investigate theoretically the far-infrared absorption of two vertically coupled quantum rings. The obtained spectrum can be described as a superimposition of inter-ring (bonding-antibonding) and intraring transitions. The two kinds of resonances have different responses to external magnetic fields, depend on different structural parameters and can be switched on and off independently by using polarized light. Structural information on the coupled quantum rings can be obtained by monitoring the magnetoabsorption spectrum of the bonding-antibonding transitions. We also show that direct imaging of the electron energy structure in a single quantum ring is possible by measuring the absorption spectrum of the ring vertically coupled to a quantum dot of similar volume.

Figure 1

FIR absorption of two vertically coupled $\mathrm{InAs}$ self-assembled QRs as a function of the top-to-base distance, at $B=0$. Unpolarized light has been used. The dashed line is a guideline for the eye showing the evolution of the bonding-antibonding resonance.

Figure 2

FIR magnetoabsorption of two small VCQRs, with $6\mathrm{nm}$ (bottom panel) and $4\mathrm{nm}$ (middle panel) top-to-base separation, using unpolarized light. The top panel shows the spectrum of a single QR for comparison. The inset shows the two-electron BAB resonances in the $d=4$ case.

Figure 3

FIR magnetoabsorption of two small VCQRs, using $z$-polarized light. (a) represents the spectra of two identical QRs (solid lines) and those of two QRs with slightly different vertical confinement (dashed lines). (b) represents the spectra of two QRs with different lateral confinement. The inset in (b) shows the energy levels of the lowest bonding and antibonding states with $m=0$ (solid lines) and $m=-1$ (dashed lines) vs the magnetic field.

Figure 4

FIR magnetoabsorption of a self-assembled QR vertically coupled to a self-assembled QD. Unpolarized light has been used. The inset shows the one-electron energy structure of the system vs $B$, with solid line arrows indicating the $\mathrm{\Delta }m=\pm 1$ transitions and the dashed line arrow the $\mathrm{\Delta }m=0$ one.