Interaction of quantum well excitons with a resonant localized excitation

We consider Wannier-Mott exciton in a semiconductor quantum well coupled via Coulomb interaction to a resonant localized excitation (a luminescent molecule or a quantum dot) placed nearby. As a result, the localized excitation can decay into the quantum well, which can be used for indirect pumping of Wannier excitons. On the other hand, Wannier excitons are scattered, and the scattering can be elastic or inelastic, depending on the strength of the dissipation in the molecule. We also show how the inelastic scattering transforms into the Förster picture of energy transfer when many molecules (quantum dots) with strong intrinsic dissipation are present.

Figure 1

A point acceptor on the surface of a semiconductor quantum well.

Figure 2

The real (solid line) and imaginary (dashed line) parts of the acceptor self-energy $\Sigma \left(E\right)$ for $L_w=L_b=10\mathrm{\AA }$, $z_0=0$, $\epsilon =6$, $\tilde{\epsilon }=1$, $m=0.76m_0$, $d^L=0.1e$, $d^Z=0$, ${\mathbf{d}}_{\Vert }^a=0$, and $d_z^a=5\mathrm{D}$.

Figure 3

The acceptor excitation weight ${\mid {\psi }_a\mid }^2$ in the discrete state for the same parameters, as in Fig. 2.

Figure 4

The elastic scattering cross section (solid line) and the capture cross section (dashed line) for the parameters of Fig. 2 and $E_a=15\mathrm{meV}$, $2{\gamma }_a∕\hslash =1{\mathrm{ps}}^{-1}$.

Figure 5

Acceptor spectral weight, given by Eq. (31), for the parameters of Fig. 2, the intrinsic dissipation in the acceptor $2{\gamma }_a∕\hslash ={\left(0.1\mathrm{ns}\right)}^{-1}$, and the acceptor level position $E_a+\Sigma \left(0\right)=-0.1\mathrm{meV}$ (solid line), 0 (dashed line), and $0.5\mathrm{meV}$ (dotted line).