Fractional-dimensional excitonic absorption theory applied to $\mathrm{V}$-groove quantum wires

A fractional-dimensional approach is applied to a realistic $\mathrm{V}$-groove quantum wire in order to calculate the excitonic absorption spectrum. An excellent agreement is obtained with much more computationally demanding models as well as with experimental photoluminescence excitation data. However, comparison with a full excitonic calculation reveals situations were the concept of fractional dimensions to some extent fails.

Figure 1

Calculated excitonic and free carrier optical densities for an electron and a hole in the first subband $\left(e_1{h}_1\right)$. The light is incident along the $z$ axis and has equal magnitude in linear polarization parallel and perpendicular to the QWR axis. A Lorentzian broadening parameter of $\mathrm{FWHM}=6\mathrm{meV}$ is used. The inset shows the $\mathrm{Al}$ concentration in the QWR region, which also reveals the size and shape of the $\mathrm{GaAs}$ QWR.

Figure 2

Calculated total optical absorption for (a) free carriers, (b) excitons described by fractional dimensions, (c) full exciton model without excitonic intersubband couplings, and (d) full exciton model including excitonic intersubband couplings. Note that the absorption intensity is multiplied with a factor of 0.52 in (d) for convenient comparison. The linear polarized light is incident along the $z$ axis, solid (dashed) lines correspond to polarization parallel (perpendicular) to the QWR axis. A Lorentzian broadening parameter of $\mathrm{FWHM}=6\mathrm{meV}$ is used.

Figure 3

Experimental PLE spectra (Ref. 11). The linear polarized light is incident along the $z$ axis; the solid (dashed) line corresponds to polarization parallel (perpendicular) to the QWR axis.