Optical response in a quantum dot superlattice nanoring under a lateral electric field

The optical absorption of a $\mathrm{GaAs}∕\mathrm{AlGaAs}$ quantum dot superlattice nanoring (QDSLNR) under a lateral dc electric field and with magnetic flux threading the ring is investigated. This structure and configuration provides a unique opportunity to study the optical response of a superlattice under an inhomogeneous electric field, which is not easily realized for general quantum well superlattices (QWSLs) but naturally realized for QDSLNRs under a homogeneous lateral electric field. It has been shown that a lateral dc electric field gives rise to a substantial change of the optical absorption spectra. Under a low field, the excitonic optical absorption is dominated by a $1s$ exciton. And with the electric field increasing, the optical absorption undergoes a transition from $1s$ excitonic absorption to 0 excitronic WSL absorption. (The number of 0, and $-1$ and $+1$ below are WSLs index.) The $-1$ and the $+1$ WSLs corresponding to the maximum effective field can also be identified. Due to the inhomogeneity of the electric field, the peaks of the $-1$ and the $+1$ WSLs are diminished and between them there exist rich and complicated structures. This is in contrast to the general QWSLs under a homogenous electric field. The complicated structures can be understood by considering the inhomogeneity of the electric field along the ring, which results in the nearest-neighbor transition, the next-nearest-neighbor transition, etc., have a different value repectively, at different sites along the ring. This may give rise to multiple WSLs. We have also shown that the line shape of the optical absorption is not sensitive to the threading magnetic flux. The threading magnetic flux only gives rise to a slight diamagnetic shift. Thus the enhancement of the sensitivity to the flux allowing for observation of the excitonic Aharanov-Bohm effect in the plain nanoring is not expected in QDSLNRs.

Figure 1

Optical density of state of QDSLNR under different electric fields $F$. (a) Optical density of state of QDSLNR under different electric fields with strength from 0 to $10\mathrm{kV}∕\mathrm{cm}$ at a step of $1.25\mathrm{kV}∕\mathrm{cm}$. The three dotted arrows labeled by 0, $-1$, and $+1$, are guides to the eye to indicate the linear shift of the WSLs with the applied field. The numbers 0, $-1$, and $+1$ are the WSL index. (b) Optical density of state of QDSLNR under different electric fields with strength from 10 to $50\mathrm{kV}∕\mathrm{cm}$ at a step of $5\mathrm{kV}∕\mathrm{cm}$.

Figure 2

Optical absorption of QDSLNR with excitonic effects under different electric fields $F$. (a) The reduction in height, broadening or splitting, and redshift of the main exciton peak induced by the applied lateral dc fields. The field's strength increases from 0 to $10\mathrm{kV}∕\mathrm{cm}$ at a step of $1.25\mathrm{kV}∕\mathrm{cm}$. (b) The increasing and redshift of the main $0\left(X\right)$ WSL and the diminishing of the $1s$ main excitonic peak induced by the applied lateral dc field. The field's strength increases from 10 to $50\mathrm{kV}∕\mathrm{cm}$ at a step of $5\mathrm{kV}∕\mathrm{cm}$. (c) The enlarged and wider energy range plot of (a) to show the details of the bottom and identification of the $0\left(X\right)$, $-1\left(X\right)$, and $+1\left(X\right)$ excitonic WSLs. The number of 0, $-1$, and $+1$ are WSL index and $X$ indicating exciton.

Figure 3

Optical absorption of QDSLNR with different threading magnetic flux $\Phi$. (a) The effect of magnetic flux on the main exciton peak in the presence of a moderate lateral dc field with field strength $5\mathrm{kV}∕\mathrm{cm}$. (b) The effect of magnetic flux on the main exciton peak in the presence of a strong lateral dc field with field strength $50\mathrm{kV}∕\mathrm{cm}$.