Binding energies of excitonic complexes in type-II quantum rings from diffusion quantum Monte Carlo calculations

Excitonic complexes in type-II quantum-ring heterostructures may be considered as artificial atoms due to the confinement of only one charge-carrier type in an artificial nucleus. Binding energies of excitons, trions, and biexcitons in these nanostructures are then effectively ionization energies of these artificial atoms. The binding energies reported here are calculated within the effective-mass approximation using the diffusion quantum Monte Carlo method and realistic geometries for gallium antimonide rings in gallium arsenide. The electrons form a halo outside the ring, with very little charge density inside the central cavity of the ring. The de-excitonization and binding energies of the complexes are relatively independent of the precise shape of the ring.

Figure 1

Ground-state total energies per hole of a single hole $\left({\mathrm{h}}^{+}\right)$, two holes $\left(2{\mathrm{h}}^{+}\right)$, an exciton $\left(\mathrm{X}\right)$, a negative trion $\left({\mathrm{X}}^{-}\right)$, a positive trion $\left({\mathrm{X}}^{+}\right)$, and a biexciton $\left(\mathrm{XX}\right)$ in a quantum ring plotted against the aspect ratio $2R_z/(r_{\mathrm{o}}-r_{\mathrm{i}})$ of the ring's cross section. The mean radius and ring volume are appropriate for the GaSb/GaAs quantum rings reported in Ref. [20]. Error bars are smaller than the size of the symbols. The exciton Rydberg $R_{\mathrm{y}}^{*}$ is $4.45\mathrm{meV}$ for the experimentally relevant geometry.

Figure 2

Expected peak positions for the excitonic complexes in a photoluminescence spectrum relative to the exciton peak, for a model of the quantum rings reported in Ref. [20]. The peak heights represent the relative stability of the complexes.

Figure 3

(a) De-excitonization energies and (b) binding energies against the aspect ratio $2R_z/(r_{\mathrm{o}}-r_{\mathrm{i}})$ of a quantum ring's cross section for different charge-carrier complexes. The mean radius and ring volume are appropriate for the GaSb/GaAs quantum rings reported in Ref. [20]. Error bars are smaller than the size of the symbols. The dashed lines shows the experimentally relevant aspect ratio [20].

Figure 4

Electronic charge density $\rho$ for (a) an exciton, (b) a negative trion, (c) a positive trion, and (d) a biexciton in the experimentally relevant quantum-ring geometry [20]. The shaded regions represent the ring and ${\rho }_m$ is the maximum density across all four plots. The free exciton Bohr radius is $a_0^{*}=12.5$ nm.